<PAGE>   1
                                  SCHEDULE 14A
                                 (RULE 14a-101)
 
                    INFORMATION REQUIRED IN PROXY STATEMENT
 
                            SCHEDULE 14A INFORMATION
          PROXY STATEMENT PURSUANT TO SECTION 14(a) OF THE SECURITIES
                     EXCHANGE ACT OF 1934 (AMENDMENT NO.  )
 
     Filed by the Registrant [X]

     Filed by a Party other than the Registrant [ ]
 
     Check the appropriate box:
 
     [ ] Preliminary Proxy Statement        [ ] Confidential, for Use of the
                                                Commission Only (as permitted by
                                                Rule 14a-6(e)(2))
     [X] Definitive Proxy Statement
 
     [ ] Definitive Additional Materials
 
     [ ] Soliciting Material Pursuant to Rule 14a-11(c) or Rule 14a-12

                               Unisys Corporation
- --------------------------------------------------------------------------------
                (Name of Registrant as Specified in Its Charter)

 
- --------------------------------------------------------------------------------
    (Name of Person(s) Filing Proxy Statement if other than the Registrant)
 
Payment of Filing Fee (Check the appropriate box):
 
     [X] No fee required.
 
     [ ] Fee computed on table below per Exchange Act Rules 14a-6(i)(4) and
         0-11.
 
     (1) Title of each class of securities to which transaction applies:
 
- --------------------------------------------------------------------------------
 
     (2) Aggregate number of securities to which transaction applies:
 
- --------------------------------------------------------------------------------
 
     (3) Per unit price or other underlying value of transaction computed
         pursuant to Exchange Act Rule 0-11 (Set forth the amount on which the
         filing fee is calculated and state how it was determined):
 
- --------------------------------------------------------------------------------
 
     (4) Proposed maximum aggregate value of transaction:
 
- --------------------------------------------------------------------------------
 
     (5) Total fee paid:
 
- --------------------------------------------------------------------------------
 
     [ ] Fee paid previously with preliminary materials.
 
     [ ] Check box if any part of the fee is offset as provided by Exchange Act
         Rule 0-11(a)(2) and identify the filing for which the offsetting fee
         was paid previously. Identify the previous filing by registration
         statement number, or the form or schedule and the date of its filing.
 
     (1) Amount previously paid:
 
- --------------------------------------------------------------------------------
 
     (2) Form, schedule or registration statement no.:
 
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<PAGE>   2
 
                                                       Unisys Corporation
                                                       Unisys Way
[UNISYS LOGO]                                          Blue Bell, PA 19424-0001
 
March 16, 1999
 
Dear Fellow Stockholder:
 
     It is my pleasure to invite you to the Unisys 1999 Annual Meeting of
Stockholders. This year's meeting will be held on Thursday, April 29, 1999 at
the Park Hyatt Philadelphia at the Bellevue, which is located at Broad and
Walnut Streets in Philadelphia, Pennsylvania. The meeting will begin at 9:30
a.m.
 
     As you will note in the enclosed annual report to stockholders, the company
continues to make very strong progress. In 1998 we accelerated revenue growth,
more than doubled earnings per share, generated strong cash flow, and exceeded
our $1 billion debt reduction target. Equally important, we laid the foundation
for future growth by investing in what I see as the three keys to our
success -- employees, customers, and reputation. Today, employee morale is
soaring, customer satisfaction is up, and our reputation in the marketplace has
improved significantly.
 
     Whether you plan to attend the annual meeting or not, I urge you to take a
moment to vote on the items in this year's proxy statement. This year, most
stockholders can vote their shares by using the Internet or the telephone.
Instructions for using these new services are on your proxy card. Of course, you
may also vote your shares by completing, signing, and returning your proxy card.
Voting by any of these means only takes a few minutes, and it will ensure that
your shares are represented at the meeting.
 
     I look forward to seeing you at the annual meeting and to reporting on our
1998 achievements and our goals for 1999.
 
                                          Sincerely,
                                          /s/ Larry A. Weinbach
                                          Lawrence A. Weinbach
                                          Chairman, President and
                                          Chief Executive Officer

<PAGE>   3
 
                                 [UNISYS LOGO]
 

                    NOTICE OF ANNUAL MEETING OF STOCKHOLDERS
 
                                 APRIL 29, 1999
 
     Unisys Corporation will hold its 1999 Annual Meeting of Stockholders at The
Park Hyatt Philadelphia at the Bellevue, Broad and Walnut Streets, Philadelphia,
Pennsylvania, on Thursday, April 29, 1999 at 9:30 a.m. to:
 
          1. elect three directors;
 
          2. ratify the selection of independent auditors for 1999; and
 
          3. transact any other business properly brought before the meeting.
 
     Only holders of Unisys Common Stock of record at the close of business on
February 22, 1999 will be entitled to vote at the Annual Meeting.
 
                                          By Order of the Board of Directors,
                                          /s/ Harold S. Barron
                                          Harold S. Barron
                                          Senior Vice President, General Counsel
                                          and Secretary
 
Blue Bell, Pennsylvania
M
arch 16, 1999
 
                                   IMPORTANT
 
YOUR VOTE IS IMPORTANT. THIS YEAR, MOST STOCKHOLDERS WILL HAVE A CHOICE OF
VOTING OVER THE INTERNET, BY TELEPHONE, OR BY USING A TRADITIONAL PROXY CARD.
PLEASE CHECK YOUR PROXY CARD OR THE INFORMATION FORWARDED BY YOUR BANK, BROKER
OR OTHER HOLDER OF RECORD TO SEE WHICH OPTIONS ARE AVAILABLE TO YOU.

<PAGE>   4
 
                               TABLE OF CONTENTS
 

<TABLE>
<S>                                                           <C>
PROXY STATEMENT
  Required Vote.............................................    1
  Voting Procedures and Revocability of Proxies.............    1
ELECTION OF DIRECTORS.......................................    2
  Information Regarding Nominees and Directors..............    2
  Board Meetings............................................    5
  Committees................................................    6
  Corporate Governance Guidelines...........................    6
  Stock Ownership Guidelines................................    7
RATIFICATION OF SELECTION OF INDEPENDENT AUDITORS...........    8
SECURITY OWNERSHIP BY CERTAIN BENEFICIAL OWNERS AND
  MANAGEMENT................................................    8
EXECUTIVE COMPENSATION......................................   10
  Summary Compensation Table................................   10
  Option Grants in Last Fiscal Year.........................   11
  Option Exercises and Fiscal Year-End Values...............   11
  Pension Plans.............................................   12
  Employment Agreements.....................................   13
  Change in Control Employment Agreements...................   13
  Indebtedness of Management................................   14
  Compensation of Directors.................................   14
REPORT OF THE CORPORATE GOVERNANCE AND COMPENSATION
  COMMITTEE.................................................   15
  Compensation Program and Policies.........................   15
  Base Salary...............................................   15
  Short-Term Incentive Payments.............................   15
  Long-Term Incentive Awards................................   16
  Compensation of the Chief Executive Officer...............   16
  Deductibility of Executive Compensation...................   16
STOCK PERFORMANCE GRAPH.....................................   17
GENERAL MATTERS.............................................   18
  Policy on Confidential Voting.............................   18
  Stockholder Proposals.....................................   18
  Electronic Access to Proxy Materials and Annual Report....   18
  Other Matters.............................................   18
</TABLE>


<PAGE>   5
 
                               UNISYS CORPORATION
 
                                PROXY STATEMENT
 
                         ANNUAL MEETING OF STOCKHOLDERS
 
                                 APRIL 29, 1999
 
     The Board of Directors of Unisys Corporation solicits your proxy for use at
the 1999 Annual Meeting of Stockholders to be held on April 29, 1999 and at any
adjournment(s). At the Annual Meeting, stockholders will be asked to elect
directors and to ratify the selection of independent auditors.
 
     The record date for the Annual Meeting is February 22, 1999. Only holders
of record of Unisys Common Stock as of the close of business on the record date
are entitled to vote at the meeting. On the record date, 261,653,650 shares of
Common Stock were outstanding. The presence, in person or by proxy, of a
majority of those shares will constitute a quorum at the meeting.
 
     This Proxy Statement, the proxy/voting instruction card, and the annual
report of Unisys, including 1998 financial statements, are being mailed and made
available on the Internet on or about March 16, 1999.
 
REQUIRED VOTE
 
     Each share of Unisys Common Stock outstanding on the record date is
entitled to one vote on each matter to be voted upon. Directors will be elected
by a plurality of the votes cast (i.e., the nominees receiving the greatest
number of votes will be elected). Abstentions and broker non-votes are not
counted for purposes of the election of directors. Ratification of the selection
of independent auditors will require the affirmative vote of a majority of
shares present, in person or by proxy, and entitled to vote. Abstentions will be
included in the vote totals for this matter, and therefore will have the same
effect as a negative vote; broker non-votes will not be included in the vote
totals and therefore will have no effect on the vote.
 
VOTING PROCEDURES AND REVOCABILITY OF PROXIES
 
     Your vote is important. Shares may be voted at the Annual Meeting only if
you are present in person or represented by proxy. Most stockholders have a
choice of voting (a) by completing a proxy/voting instruction card and mailing
it in the postage-paid envelope provided, (b) over the Internet, or (c) by
telephone using a toll-free telephone number. Check your proxy card or the
information forwarded by your bank, broker or other holder of record to see
which options are available to you and to obtain the applicable web site or
telephone number. Please be aware that if you vote over the Internet, you may
incur costs associated with electronic access, such as usage charges from
Internet access providers and telephone companies, for which you will be
responsible.
 
     The telephone and Internet voting procedures are designed to authenticate
stockholders' identities by use of a control number, to allow stockholders to
give their voting instructions, and to confirm that stockholders' instructions
have been recorded properly. The Company has been advised by counsel that the
telephone and Internet voting procedures are consistent with the requirements of
applicable law.

<PAGE>   6
 
     You may revoke your proxy at any time before it is exercised by writing to
the Secretary of Unisys, by timely delivery of a properly executed later-dated
proxy (including an Internet or telephone vote), or by voting in person at the
meeting.
 
     The method by which you vote will in no way limit your right to vote at the
meeting if you later decide to attend in person. If your shares are held in the
name of a bank, broker or other holder of record, you must obtain a proxy,
executed in your favor, from the holder of record, to be able to vote at the
meeting.
 
     If you properly complete and return your proxy, and do not revoke it, the
proxy holders will vote your shares in accordance with your instructions. If
your properly completed proxy gives no instructions, the proxy holders will vote
your shares FOR the election of directors, FOR the selection of independent
auditors and in their discretion on any other matters that properly come before
the Annual Meeting.
 
     If you are a participant in the Unisys Savings Plan, the proxy/voting
instruction card will serve as voting instructions to the plan trustee for any
whole shares of Unisys Common Stock credited to your account as of February 22,
1999. The trustee will vote those shares in accordance with your instructions if
it receives your completed proxy by April 23, 1999. If the proxy is not timely
received, or if you give no instructions on a matter to be voted upon, the
trustee will vote the shares credited to your account in the same proportion as
it votes those shares for which it received proper instructions from other
participants.
 
                             ELECTION OF DIRECTORS
 
     The Board of Directors currently consists of ten members, divided into
three classes. One class of directors is elected each year to hold office for a
three-year term. The three directors whose terms expire in 1999, J.P. Bolduc,
James J. Duderstadt, and Kenneth A. Macke, have been nominated for reelection.
The remaining seven directors will continue to serve as set forth below. Each of
the nominees has agreed to serve as a director if elected, and Unisys believes
that each nominee will be available to serve. However, the proxy holders have
discretionary authority to cast votes for the election of a substitute should
any nominee not be available to serve as a director.
 
INFORMATION REGARDING NOMINEES AND DIRECTORS
 
     The names and ages of the nominees and directors, their principal
occupations and employment during the past five years, and other data regarding
them are as follows.
 
                                        2

<PAGE>   7
 
                NOMINEES FOR ELECTION TO THE BOARD OF DIRECTORS
 
[BOLDUC PHOTO]
                  J. P. BOLDUC
                  Mr. Bolduc, 59, is Chairman and Chief Executive Officer of JPB
                  Enterprises, Inc., a merchant banking, venture capital, and
                  real estate investment holding company with interests in the
                  food, beverage, real estate, retail, and manufacturing
                  industries. He previously served in the positions of Vice
                  Chairman, Chief Operating Officer, President and Chief
                  Executive Officer of W. R. Grace & Co., a specialty chemicals
                  and health care company, from 1986 to 1995. He is a Director
                  of Brothers Gourmet Coffees, Inc., Marshall & Ilsley
                  Corporation, Proudfoot PLC, and Sundstrand Corporation. He has
                  served as a Director of Unisys since 1992 and is a member of
                  the Finance Committee and the Nominating Committee of the
                  Board of Directors.
 
[DUDERSTADT PHOTO]
                  JAMES J. DUDERSTADT
                  Dr. Duderstadt, 56, is President Emeritus and University
                  Professor of Science and Engineering at the University of
                  Michigan. He is a Director of CMS Energy Corporation. He has
                  served as a Director of Unisys since 1990 and is a member of
                  the Audit Committee and the Nominating Committee of the Board
                  of Directors.
 
[MACKE PHOTO]
                  KENNETH A. MACKE
                  Mr. Macke, 60, is General Partner of Macke Partners, a venture
                  capital firm. He previously served as Chairman and Chief
                  Executive Officer of Dayton Hudson Corporation, a general
                  merchandise retailer, from 1984 to 1994. He is a Director of
                  Fingerhut Companies, Inc., General Mills, Inc., and Select
                  Comfort Corporation. He has served as a Director of Unisys
                  since 1989 and is a member of the Corporate Governance and
                  Compensation Committee and the Nominating Committee of the
                  Board of Directors.
 
                                        3

<PAGE>   8
 
             MEMBERS OF THE BOARD OF DIRECTORS CONTINUING IN OFFICE
                             TERM EXPIRING IN 2000
 
[FOSLER PHOTO]
                  GAIL D. FOSLER
                  Ms. Fosler, 51, is Senior Vice President and Chief Economist
                  of The Conference Board, a business-sponsored, nonprofit
                  research organization. She is a Director of H. B. Fuller
                  Company and a Trustee of the John Hancock Mutual Funds. She
                  has served as a Director of Unisys since 1993 and is a member
                  of the Finance Committee and the Nominating Committee of the
                  Board of Directors.
 
[GOODES PHOTO]
                  MELVIN R. GOODES
                  Mr. Goodes, 63, is a Director and Chairman and Chief Executive
                  Officer of Warner-Lambert Company, a diversified worldwide
                  health care, pharmaceutical, and consumer products company. He
                  is a Director of Ameritech Corporation and Chase Manhattan
                  Corporation. He has served as a Director of Unisys since 1987
                  and is a member of the Corporate Governance and Compensation
                  Committee and the Nominating Committee of the Board of
                  Directors.
 
[HUSTON PHOTO]
                  EDWIN A. HUSTON
                  Mr. Huston, 60, is Senior Executive Vice President-Finance and
                  Chief Financial Officer of Ryder System, Inc., an
                  international highway transportation services company. He has
                  served as a Director of Unisys since 1993 and is a member of
                  the Corporate Governance and Compensation Committee and the
                  Nominating Committee of the Board of Directors.
 
[McCLEMENTS PHOTO]
                  ROBERT MCCLEMENTS, JR.
                  Mr. McClements, 70, is a retired Chairman, President and Chief
                  Executive Officer of Sun Company, Inc., a diversified energy
                  company. He is a Director of Bethlehem Steel Corporation. He
                  has served as a Director of Unisys since 1991 and is a member
                  of the Audit Committee and the Nominating Committee of the
                  Board of Directors.
 
                                        4

<PAGE>   9
 
             MEMBERS OF THE BOARD OF DIRECTORS CONTINUING IN OFFICE
                             TERM EXPIRING IN 2001
 
[DUQUES PHOTO]
                  HENRY C. DUQUES
                  Mr. Duques, 55, is a Director and Chairman and Chief Executive
                  Officer of First Data Corporation, an electronic payments and
                  information management company. He is a Director of
                  theglobe.com, inc. He has served as a Director of Unisys since
                  February 1998 and is a member of the Finance Committee and the
                  Nominating Committee of the Board of Directors.
 
[MARTIN PHOTO]
                  THEODORE E. MARTIN
                  Mr. Martin, 59, is a retired President and Chief Executive
                  Officer of Barnes Group Inc., a manufacturer and distributor
                  of automotive and aircraft components and maintenance
                  products. He has also held the position of Executive Vice
                  President-Operations of that company. He is a Director of
                  Ingersoll-Rand Company and RJR Nabisco Holdings Corp. He has
                  served as a Director of Unisys since 1995 and is a member of
                  the Audit Committee and the Nominating Committee of the Board
                  of Directors.
 
[WEINBACH PHOTO]
                  LAWRENCE A. WEINBACH
                  Mr. Weinbach, 59, is Chairman of the Board, President and
                  Chief Executive Officer of Unisys. He previously served in the
                  position of Managing Partner-Chief Executive of Andersen
                  Worldwide, a global professional services organization. He has
                  served as a Director of Unisys since 1997.
 
BOARD MEETINGS
 
     The Board of Directors held seven meetings in 1998. During 1998, all
directors attended at least 75 percent of the meetings of the Board of Directors
and standing Committees on which they served.
 
                                        5

<PAGE>   10
 
COMMITTEES
 
     The Board of Directors has a standing Audit Committee, Corporate Governance
and Compensation Committee, and Nominating Committee.
 
     The Audit Committee reviews compliance with Company policies, reviews
internal control procedures, recommends to the Board of Directors the firm of
independent auditors to serve the Company, reviews the scope, fees and results
of the audit by the independent auditors, and reviews the internal audit
organization and annual audit plan. The Audit Committee held four meetings in
1998. Its members are Dr. Duderstadt, Mr. Martin, and Mr. McClements.
 
     The Corporate Governance and Compensation Committee oversees the Company's
corporate governance, the Company's executive management structure, the
compensation-related policies and programs involving the Company's executive
management, and the level of compensation and benefits of officers and key
employees. It also oversees the Company's diversity programs. The Corporate
Governance and Compensation Committee held seven meetings in 1998. Its members
are Mr. Goodes, Mr. Huston, and Mr. Macke.
 
     The Nominating Committee identifies and reviews candidates and recommends
to the Board of Directors nominees for membership on the Board of Directors. In
fulfilling this responsibility, the Nominating Committee will consider
recommendations received from stockholders and other qualified sources.
Stockholder recommendations must be in writing and addressed to the Chairman of
the Nominating Committee, c/o Corporate Secretary, Unisys Corporation, Unisys
Way, Blue Bell, Pennsylvania 19424. If a stockholder intends to make a
nomination at an annual meeting, the Company's bylaws require that the
stockholder deliver a notice to the Company not less than 90 days prior to the
meeting setting forth (i) the name, age, business and residence addresses of
each nominee, (ii) the principal occupation or employment of each nominee, (iii)
the number of shares of Unisys capital stock beneficially owned by each nominee,
(iv) a statement that the nominee is willing to be nominated, and (v) any other
information concerning each nominee that would be required by the Securities and
Exchange Commission in a proxy statement soliciting proxies for the election of
the nominee. The Nominating Committee held three meetings in 1998. All directors
other than Mr. Weinbach are members of the Nominating Committee.
 
     The Board has also designated a standing Finance Committee and may
establish other committees from time to time.
 
CORPORATE GOVERNANCE GUIDELINES
 
     The Board of Directors has adopted Guidelines on Significant Corporate
Governance Issues. Among other matters, these Guidelines cover the following:
 
          1. A majority of the Board of Directors should be independent
     directors. Interlocking directorships should be avoided, and directors
     should not, except in rare circumstances approved by the Board, draw any
     consulting, legal or other fees from the Company. The independence of
     outside directors is reviewed annually by the Corporate Governance and
     Compensation Committee.
 
          2. Membership on the Audit, Corporate Governance and Compensation, and
     Nominating Committees is limited to outside directors.
 
                                        6

<PAGE>   11
 
           3. Directors may not stand for election after age 70 or continue to
     serve beyond age 72.
 
           4. Directors should offer their resignations upon a change in
     position, including retirement, from the position they held when they were
     elected to the Board. In addition, if the Company's chief executive officer
     resigns from that position, he is expected to offer his resignation from
     the Board at the same time.
 
           5. The Nominating Committee is responsible for determining the
     appropriate skills and characteristics required of Board members and will
     consider issues of diversity, age, and skills in its assessment of the
     needs of the Board. The Corporate Governance and Compensation Committee
     maintains an orientation program for new directors.
 
           6. The Corporate Governance and Compensation Committee is responsible
     for providing an annual assessment of the Board's performance and of its
     contribution as a whole.
 
           7. The outside directors have the opportunity to meet in executive
     session, apart from the chief executive officer and other members of
     management, at any time. Either the outside director serving as the
     chairman of the Corporate Governance and Compensation Committee or the
     outside director serving as the chairman of the Finance Committee assumes
     the responsibility of chairing such meetings.
 
           8. The outside directors meet annually in executive session to review
     the performance of the chief executive officer. The evaluation is led by
     the Corporate Governance and Compensation Committee and is based on
     objective criteria, including performance of the business, accomplishment
     of long-term strategic objectives, and development of management. The
     evaluation is used by the Corporate Governance and Compensation Committee
     in its consideration of the compensation of the chief executive officer.
 
           9. The chief executive officer is expected to provide an annual
     report on succession planning to the Corporate Governance and Compensation
     Committee.
 
          10. Board members have complete access to Unisys management. Members
     of senior management who are not Board members regularly attend Board
     meetings, and the Board encourages senior management, from time to time, to
     bring into Board meetings other managers who can provide additional
     insights into the matters under discussion.
 
STOCK OWNERSHIP GUIDELINES
 
     In 1998, the Board established stock ownership guidelines for both
directors and executive officers in order to more closely link their interests
with those of stockholders. Under the guidelines, directors are expected to own,
within a five-year period, Unisys stock or stock units having a value equal to
four times their annual retainer. Executive officers are expected to own stock
or stock units having a value equal to a multiple of base salary as follows:
chief executive officer -- four times; executive and senior vice
presidents -- two times; vice presidents -- one times. They have either three or
five years to achieve the minimum levels, depending on the date they became an
executive officer. Restricted shares and stock options, including vested stock
options, do not count toward fulfillment of the ownership guidelines.
 
                                        7

<PAGE>   12
 
               RATIFICATION OF SELECTION OF INDEPENDENT AUDITORS
 
     The Board of Directors, upon the recommendation of the Audit Committee, has
selected the firm of Ernst & Young LLP as independent auditors to audit the
Company's books and accounts for the year ending December 31, 1999 and
recommends ratification of this selection by the stockholders. Ernst & Young LLP
has served as independent auditors for Unisys since the merger of Burroughs
Corporation and Sperry Corporation in 1986, having previously served in that
capacity for Sperry Corporation. Its representatives will be present at the
Annual Meeting and will have the opportunity to make a statement if they desire
to do so and to respond to appropriate questions asked by stockholders.
 
     The Board of Directors considers Ernst & Young LLP to be well qualified to
serve as the independent auditors for Unisys. If, however, stockholders do not
ratify the selection of Ernst & Young LLP, the Board will reconsider the
appointment.
 
     THE BOARD OF DIRECTORS RECOMMENDS A VOTE "FOR" THE PROPOSAL TO RATIFY THE
SELECTION OF ERNST & YOUNG LLP AS INDEPENDENT AUDITORS FOR 1999. PROXIES
SOLICITED BY THE BOARD OF DIRECTORS WILL BE SO VOTED UNLESS STOCKHOLDERS
OTHERWISE SPECIFY IN THEIR PROXIES.
 

         SECURITY OWNERSHIP BY CERTAIN BENEFICIAL OWNERS AND MANAGEMENT
 
     Shown below is information with respect to persons or groups that
beneficially own more than five percent of Unisys Common Stock. This information
is derived from Schedules 13G filed by such persons or groups in February 1999.
 

<TABLE>
<CAPTION>
N
AME AND ADDRESS OF                                           NUMBER OF SHARES    PERCENT
BENEFICIAL OWNER                                              OF COMMON STOCK     OF CLASS
- -------------------                                           ----------------    --------
<S>                                                           <C>                 <C>
FMR Corp. ..................................................     38,711,613(1)     14.976
Edward C. Johnson 3d
Abigail P. Johnson
Fidelity Management & Research Company
82 Devonshire Street, Boston, MA 02109
Tiger Management L.L.C. ....................................     16,079,100(2)        6.3
Tiger Performance L.L.C.
Julian H. Robertson, Jr.
101 Park Avenue, New York, NY 10178
AIM Management Group, Inc. .................................     13,660,472(2)       5.37
AMVESCAP Group Services, Inc.
AMVESCAP PLC
AVZ, Inc.
INVESCO (NY) Asset Management, Inc.
INVESCO Capital Management, Inc.
INVESCO Funds Group, Inc.
INVESCO Management & Research, Inc.
INVESCO North American Holdings, Inc.
INVESCO Realty Advisers, Inc.
INVESCO, Inc.
11 Devonshire Square, London EC2M 4YR, England
</TABLE>

 
- ---------------
(1) Of the shares shown, 3,281,218 represent shares issuable upon conversion of
    the Company's convertible debt securities and preferred stock. Sole
    dispositive power has been reported for 38,711,613 shares. Sole voting power
    has been reported for 1,853,954 shares.
 
(2) Shared voting power and shared dispositive power have been reported for all
    shares shown.
 
                                        8

<PAGE>   13
 
     Shown below are the number of shares of Unisys Common Stock (or stock
units) beneficially owned as of March 1, 1999, by all directors and nominees,
each of the executive officers named on page 10, and all directors and executive
officers of Unisys as a group. No individual or group named below beneficially
owns more than one percent of the outstanding shares of Unisys Common Stock.
 

<TABLE>
<CAPTION>
                                                                        ADDITIONAL SHARES OF
                                               NUMBER OF SHARES         COMMON STOCK DEEMED
BENEFICIAL OWNER                             OF COMMON STOCK(1)(2)    BENEFICIALLY OWNED(1)(3)
- ----------------                             ---------------------    ------------------------
<S>                                          <C>                      <C>
J. P. Bolduc...............................           11,888                        --
Robert H. Brust............................           76,298                    66,250
James J. Duderstadt........................           10,150                        --
Henry C. Duques............................            1,441                        --
Gail D. Fosler.............................           22,866                        --
Gerald A. Gagliardi........................           58,191                    56,250
George R. Gazerwitz........................           58,790                    60,000
Melvin R. Goodes...........................           11,116                        --
Edwin A. Huston............................           11,150                        --
Kenneth A. Macke...........................           37,257                        --
Theodore E. Martin.........................           17,950                        --
Robert McClements, Jr......................           17,416                        --
Lawrence C. Russell........................           70,848                   287,500
Lawrence A. Weinbach.......................          254,670                   312,500
All directors and executive officers as
  a group..................................          953,339                 1,349,951
</TABLE>

 
- ---------------
 
(1) Includes shares reported by directors and executive officers as held
    directly or in the names of spouses, children or trusts as to which
    beneficial ownership may have been disclaimed.
 
(2) Includes shares held under the Unisys Savings Plan, a qualified plan under
    Sections 401(a) and 401(k) of the Internal Revenue Code, as follows: Mr.
    Brust, 1,071; Mr. Gagliardi, 599; Mr. Gazerwitz, 1,653; Mr. Russell, 8; Mr.
    Weinbach, 27; executive officers as a group, 6,762. With respect to such
    shares, plan participants have authority to direct voting. Also includes
    restricted shares, which may be voted but may not be sold or pledged, as
    follows: Mr. Brust, 75,000; Mr. Weinbach, 84,881; executive officers as a
    group, 159,881. Also includes stock units deferred under the Deferred
    Compensation Plan For Executives of Unisys Corporation as follows: Mr.
    Gagliardi, 8,000; Mr. Gazerwitz, 13,000; executive officers as a group,
    163,109. Deferred stock units are payable in shares of Unisys common stock
    upon termination of employment or any date at least five years after the
    deferral. They may not be voted. Also includes Stock Units, as described on
    page 14, for directors as follows: Mr. Bolduc, 8,888; Dr. Duderstadt, 9,100;
    Mr. Duques, 1,441; Ms. Fosler, 7,716; Mr. Goodes, 10,916; Mr. Huston,
    10,150; Mr. Macke, 36,057; Mr. Martin, 17,950; Mr. McClements, 17,416.
 
(3) Shares shown are shares subject to options exercisable within 60 days
    following March 1, 1999.
 
                                        9

<PAGE>   14
 

                             EXECUTIVE COMPENSATION
 
SUMMARY COMPENSATION TABLE
 
     The following table sets forth information concerning the annual and
long-term compensation paid to the chief executive officer and the other four
most highly compensated executive officers of Unisys in 1998 (the "Named
Officers"), for services rendered in all capacities to Unisys for 1998, 1997 and
1996.
 

<TABLE>
<CAPTION>
                                                                                     LONG-TERM COMPENSATION
                                                                          ---------------------------------------------
                          ANNUAL COMPENSATION                                     AWARDS                  PAYOUTS
- -----------------------------------------------------------------------   -----------------------   -------------------
                                                                OTHER     RESTRICTED   SECURITIES
                                                               ANNUAL       STOCK      UNDERLYING    LTIP     ALL OTHER
                                                               COMPEN-     AWARD(S)     OPTIONS/    PAYOUTS    COMPEN-
           NAME AND                   SALARY(1)   BONUS(1)    SATION(2)      (3)        SARS(4)       (4)     SATION(5)
      PRINCIPAL POSITION        YEAR     ($)         ($)         ($)         ($)          (#)         ($)        ($)
      ------------------        ----  ---------   ---------   ---------   ----------   ----------   -------   ---------
<S>                             <C>   <C>         <C>         <C>         <C>          <C>          <C>       <C>
Lawrence A. Weinbach(6).......  1998  1,200,000   1,800,000   1,332,709          --      250,000      --       161,800
  Chairman, President and       1997    327,692   1,992,000     766,742   2,058,364    1,000,000      --            --
  Chief Executive Officer
 
Gerald A. Gagliardi...........  1998    450,000     270,000       9,333          --       75,000      --           800
  Executive Vice President      1997    426,669     194,000      61,788          --       60,000      --        87,310
                                1996    397,504     205,000       8,198     594,000       60,000      --        25,140
 
George R. Gazerwitz...........  1998    435,674     325,000       6,020          --      100,000      --        60,790
  Executive Vice President      1997    350,004     256,000      65,506          --       60,000      --        85,116
                                1996    283,554     145,000          --     472,928       50,000      --        15,616
 
Lawrence C. Russell...........  1998    450,000     270,000      11,087          --      100,000      --       100,800
  Executive Vice President      1997    450,000     216,000      12,095          --       60,000      --       260,900
                                1996    450,000     270,000     163,575     682,103       60,000      --            --
 
Robert H. Brust(7)............  1998    395,840     275,000      20,836          --       65,000      --           800
  Senior Vice President         1997    320,313     216,000     186,566     867,188      100,000      --        54,250
  and Chief Financial Officer
</TABLE>

 
- ---------------
 
(1) Amounts shown include compensation deferred under the Unisys Savings Plan or
    the Deferred Compensation Plan for Executives of Unisys Corporation.
 
(2) Amounts shown for Mr. Weinbach for 1998 are tax reimbursements and personal
    benefits, including $42,461 for relocation. All amounts shown for the other
    Named Officers for 1998 are tax reimbursements.
 
(3) Amounts shown are the dollar value of restricted stock awards based on the
    closing market price of Unisys Common Stock on the date of grant. At
    December 31, 1998, the number and value of restricted share holdings for
    each of the Named Officers were as follows: Mr. Weinbach - 84,881 shares,
    $2,923,089; Mr. Gagliardi - 80,000 shares, $2,755,000; Mr.
    Gazerwitz - 65,000 shares, $2,238,438; Mr. Russell - 90,947 shares,
    $3,131,987; Mr. Brust - 75,000 shares, $2,582,813. Mr. Weinbach was
    originally awarded 169,762 restricted shares in 1997, of which 84,881 shares
    were vested at December 31, 1998. The remaining shares will vest in two
    installments, on September 23, 1999 and September 23, 2000. Mr. Brust's 1997
    restricted stock award will vest on March 1, 2000. The restricted stock
    awards to the other Named Officers vested on March 1, 1999.
 
(4) Although the Company's long-term incentive plan permits grants of
    free-standing stock appreciation rights and the payment of performance
    awards, no such grants or payments were made to any of the Named Officers
    during the years presented.
 
(5) Amounts shown for 1998 for all Named Officers include $800 in Company
    matching contributions under the Unisys Savings Plan. Amounts shown for Mr.
    Weinbach and Mr. Gazerwitz for 1998 also include the full amount of premiums
    paid by Unisys for life insurance under split-dollar arrangements. Amount
    shown for Mr. Russell for 1998 also includes $100,000 in respect of the
    incentive forfeiture payments referred to on page 13.
 
(6) Mr. Weinbach joined Unisys in September 1997.
 
(7) Mr. Brust joined Unisys in February 1997.
 
                                       10

<PAGE>   15
 
OPTION GRANTS IN LAST FISCAL YEAR
 
     The following table sets forth information on grants of stock options
during 1998 to the Named Officers. No stock appreciation rights were granted
during 1998.
 

<TABLE>
<CAPTION>
                                                                               POTENTIAL REALIZABLE VALUE AT
                                                                                  ASSUMED ANNUAL RATES OF
                                                                                 STOCK PRICE APPRECIATION
                             INDIVIDUAL GRANTS                                      FOR OPTION TERMS(1)
- ----------------------------------------------------------------------------   -----------------------------
                             NUMBER OF       % OF
                             SECURITIES     TOTAL
                             UNDERLYING    OPTIONS     EXERCISE
                              OPTIONS     GRANTED TO   OR BASE
                             GRANTED(2)   EMPLOYEES    PRICE(3)   EXPIRATION
           NAME                 (#)        IN 1998      ($/SH)     DATE(4)     0%($)     5%($)      10%($)
           ----              ----------   ----------   --------   ----------   -----   ---------   ---------
<S>                          <C>          <C>          <C>        <C>          <C>     <C>         <C>
Lawrence A. Weinbach.......   250,000        4.7       22.7188     4/22/08      --     3,578,211   8,746,738
Gerald A. Gagliardi........    75,000        1.4       22.7188     4/22/08      --     1,073,463   2,624,021
George R. Gazerwitz........   100,000        1.9       22.7188     4/22/08      --     1,431,284   3,498,695
Lawrence C. Russell........   100,000        1.9       22.7188     4/22/08      --     1,431,284   3,498,695
Robert H. Brust............    65,000        1.2       22.7188     4/22/08      --       930,335   2,347,988
</TABLE>

 
- ---------------
 
(1) Illustrates value that might be realized upon exercise of options
    immediately prior to the expiration of their term, assuming specified annual
    rates of appreciation on Unisys Common Stock over the term of the options.
    Assumed rates of appreciation are not necessarily indicative of future stock
    performance.
 
(2) Options were granted on April 22, 1998. Options become exercisable in four
    equal annual installments, beginning one year after the date of grant.
    Options become immediately exercisable in the event of a change in control
    (as defined in the long-term incentive plan).
 
(3) The exercise price per share is the fair market value (calculated as the
    average of the high and low sales prices reported on the Composite Tape for
    New York Stock Exchange Listed Companies) of a share of Unisys Common Stock
    on the date of grant. Options may be exercised with cash and/or with other
    shares of Unisys Common Stock or with any other form of consideration
    permitted by the Corporate Governance and Compensation Committee.
 
(4) The options were granted for a term of ten years, subject to earlier
    termination in certain events related to termination of employment.
 
OPTION EXERCISES AND FISCAL YEAR-END VALUES
 
     The following table sets forth information with respect to option exercises
during 1998 and unexercised stock options held by the Named Officers at December
31, 1998.
 

<TABLE>
<CAPTION>
                                                         NUMBER OF SECURITIES          VALUE OF UNEXERCISED
                                                        UNDERLYING UNEXERCISED             IN-THE-MONEY
                                                              OPTIONS AT                    OPTIONS AT
                              SHARES                       DECEMBER 31, 1998           DECEMBER 31, 1998(1)
                             ACQUIRED       VALUE                 (#)                           ($)
                            ON EXERCISE   REALIZED    ---------------------------   ---------------------------
           NAME                 (#)          ($)      EXERCISABLE   UNEXERCISABLE   EXERCISABLE   UNEXERCISABLE
           ----             -----------   ---------   -----------   -------------   -----------   -------------
<S>                         <C>           <C>         <C>           <C>             <C>           <C>
Lawrence A. Weinbach......     --            --         250,000       1,000,000      5,664,050     19,921,825
Gerald A. Gagliardi.......   108,459      1,187,128          --         157,500             --      3,174,841
George R. Gazerwitz.......   196,483      2,538,381       3,750         177,500        103,828      3,323,120
Lawrence C. Russell.......     --            --         232,500         237,500      6,647,344      5,078,901
Robert H. Brust...........     --            --          25,000         140,000        692,188      2,838,278
</TABLE>

 
- ---------------
 
(1) Difference between the closing price reported on the Composite Tape for New
    York Stock Exchange Listed Companies for Unisys Common Stock at December 31,
    1998 and the exercise price.
 
                                       11

<PAGE>   16
 
PENSION PLANS
 
     The table below shows the aggregate annual amounts at age 65 that would be
received from the Unisys Pension Plan (the "Pension Plan"), the Supplemental
Executive Retirement Plan (the "Supplemental Plan"), and the Elected Officer
Pension Plan (the "Officer Plan").
 
     The Pension Plan and Supplemental Plan generally are available to all
employees located in the United States. The Officer Plan is available to
officers, including the Named Officers, who satisfy certain minimum service
requirements. The aggregate pension amount payable under the Officer Plan is
offset by benefits paid under the Pension Plan, the Supplemental Plan and any
applicable subsidiary plan. The amounts shown in the table are computed on a
single life annuity basis and are subject to a reduction equal to 50% of the
participant's primary social security benefit.
 

<TABLE>
<CAPTION>
                                                 YEARS OF SERVICE
     ASSUMED FINAL       -----------------------------------------------------------------
  AVERAGE COMPENSATION      5          10         15         20         25      30 OR MORE
  --------------------   --------   --------   --------   --------   --------   ----------
  <S>                    <C>        <C>        <C>        <C>        <C>        <C>
       $  200,000        $ 40,000   $ 80,000   $ 90,000   $100,000   $110,000   $  120,000
          300,000          60,000    120,000    135,000    150,000    165,000      180,000
          400,000          80,000    160,000    180,000    200,000    220,000      240,000
          500,000         100,000    200,000    225,000    250,000    275,000      300,000
          600,000         120,000    240,000    270,000    300,000    330,000      360,000
          700,000         140,000    280,000    315,000    350,000    385,000      420,000
          800,000         160,000    320,000    360,000    400,000    440,000      480,000
          900,000         180,000    360,000    405,000    450,000    495,000      540,000
        1,000,000         200,000    400,000    450,000    500,000    550,000      600,000
        1,100,000         220,000    440,000    495,000    550,000    605,000      660,000
        1,200,000         240,000    480,000    540,000    600,000    660,000      720,000
        1,300,000         260,000    520,000    585,000    650,000    715,000      780,000
        1,400,000         280,000    560,000    630,000    700,000    770,000      840,000
        1,500,000         300,000    600,000    675,000    750,000    825,000      900,000
        1,600,000         320,000    640,000    720,000    800,000    880,000      960,000
        1,700,000         340,000    680,000    765,000    850,000    935,000    1,020,000
</TABLE>

 
     Final Average Compensation generally corresponds to the amounts shown in
the Summary Compensation Table under the headings Salary and Bonus. However,
Final Average Compensation is calculated using the individual's highest 60
consecutive months of compensation out of the final 120 months of employment and
thus will differ somewhat from the amounts shown in the Summary Compensation
Table. Final Average Compensation for the eligible Named Officers as of March 1,
1999 is as follows: G. A. Gagliardi - $520,966; G. R. Gazerwitz - $491,969; L.
C. Russell - $691,800; R. H. Brust - $636,909. Full years of credited service
under the pension plans for the eligible Named Officers as of March 1, 1998 are
as follows: G. A. Gagliardi - 27 years; G. R. Gazerwitz - 17 years; L. C.
Russell - 3 years; R. H. Brust - 1 year.
 
     Pursuant to the employment agreement described below, Lawrence A. Weinbach
is vested in an annual pension benefit as follows: 0-3 years of
service - $350,000; 4 years - $570,000; 5 years - $710,000; 6 years - $860,000;
7 or more years - $1,000,000.
 
                                       12

<PAGE>   17
 
EMPLOYMENT AGREEMENTS
 
     On September 23, 1997, the Company entered into a five-year employment
agreement with Lawrence A. Weinbach, covering the terms and conditions of Mr.
Weinbach's employment as Chairman of the Board, President and Chief Executive
Officer. The agreement provides for a minimum base salary of $1,200,000 per
year, subject to annual review by the Corporate Governance and Compensation
Committee, and eligibility for an annual bonus award at a target bonus level of
not less than 100% of base salary. The actual bonus payable, if any, is to be
determined by the Corporate Governance and Compensation Committee in its sole
discretion, except that, for the 1998 and 1999 award years, Mr. Weinbach is
guaranteed a minimum bonus equal to 100% of the base salary paid to him in that
year. Mr. Weinbach is eligible to participate in the benefit programs generally
made available to executive officers, is entitled to the pension benefits
discussed above, and is eligible to receive stock option and other long-term
incentive awards under the Company's long-term incentive plan. If Mr. Weinbach's
employment is terminated under certain circumstances, the agreement provides for
him to receive continued payment of his base salary for the remainder of the
term (but in no event less than one year's base salary) and, for the one-year
period following the date of termination, a bonus in an amount equal to his
target bonus percentage times the base salary paid during such period. He will
also be entitled to continued medical and dental coverage through the remaining
term of the agreement, full vesting in outstanding awards under the long-term
incentive plan, and one additional year of service for pension purposes. Salary
continuation amounts paid to Mr. Weinbach after two years from the date of
employment termination will be reduced by the amount of any cash compensation he
receives for services rendered to any entity other than Unisys. Mr. Weinbach is
also party to a change in control agreement with the Company, as described
below. He is not entitled to receive duplicate payments under the change in
control agreement and his employment agreement.
 
     Effective November 1995, the Company entered into a three-year employment
agreement with Lawrence C. Russell, covering the terms and conditions of his
employment as Executive Vice President of Unisys and President of Unisys
Information Services. Under the agreement, Mr. Russell was entitled to an annual
base salary of $450,000 and was eligible for an annual bonus at a target of not
less than 60% of base salary. The agreement provided that the actual bonus
amount could vary from zero to 150% of target. The agreement expired in
accordance with its terms in November 1998. As part of Mr. Russell's continued
employment with the Company, he will be entitled under the original contract to
receive two payments of $100,000 each in 1999 and 2000, to compensate him for
the value of incentives forfeited from his previous employment.
 
CHANGE IN CONTROL EMPLOYMENT AGREEMENTS
 
     The Company has entered into change in control employment agreements with
its executive officers including the Named Officers. The agreements are intended
to retain the services of these executives and provide for continuity of
management in the event of any actual or threatened change in control. A change
in control is generally defined as (i) the acquisition of 20% or more of Unisys
Common Stock, (ii) a change in the majority of the Board of Directors unless
approved by the incumbent directors (other than as a result of a contested
election), and (iii) certain reorganizations, mergers, consolidations,
liquidations or dissolutions. Each agreement has a term ending on the third
anniversary of the date of the change in control. These agreements, which are
the same in substance for each executive, provide that in the event of a change
in control each executive will have specific rights and receive certain
 
                                       13

<PAGE>   18
 
benefits. Those benefits include the right to continue in the Company's employ
during the term, performing comparable duties to those being performed
immediately prior to the change in control and at compensation and benefit
levels that are at least equal to the compensation and benefit levels in effect
immediately prior to the change in control. Upon a termination of employment
under certain circumstances following a change in control, the terminated
executive will be entitled to receive special termination benefits, including a
lump sum payment equal to three years base salary and bonus and the actuarial
value of the pension benefit the executive would have accrued had the executive
remained employed for three years following the termination date. The special
termination benefits are payable if the Company terminates the executive without
cause, the executive terminates employment for certain enumerated reasons
(including a reduction in the executive's compensation or responsibilities or a
change in the executive's job location), or the executive voluntarily terminates
employment for any reason during the 30-day period following the first
anniversary of the date of the change in control. If any payment or distribution
by the Company to the executive is determined to be subject to the excise tax
imposed by Section 4999 of the Internal Revenue Code, the executive is entitled
to receive a payment on an after-tax basis equal to the excise tax imposed. The
executive is under no obligation to mitigate amounts payable under these
agreements, and to the extent the executive has a separate employment agreement
with the Company with conflicting rights, the executive is allowed the greater
entitlement.
 
INDEBTEDNESS OF MANAGEMENT
 
     In 1996, the Company made a four-year, interest-free loan to Lawrence C.
Russell. The loan was made in connection with his purchase of a principal
residence upon relocation and is secured by a first mortgage. At March 1, 1999
the principal amount outstanding was $141,500. The maximum amount outstanding
during the period between January 1, 1998 and March 1, 1999 was $212,250.
 
COMPENSATION OF DIRECTORS
 
     The Company's non-employee directors receive an annual retainer of $35,000,
an annual attendance fee of $10,000 for regularly scheduled Board and Committee
meetings, and a meeting fee of $1,000 for attendance at each Board and Committee
meeting held on other than a regularly scheduled meeting day. The annual
retainer and annual meeting fee are paid in monthly installments, with 50% of
each installment paid in cash and 50% in the form of common stock equivalent
units ("Stock Units"). The value of each Stock Unit at any point in time is
equal to the value of one share of Unisys Common Stock. Stock Units are recorded
in a memorandum account maintained for each director. A director's Stock Unit
account is payable upon termination of service, or at any date at least five
years after the Stock Units are awarded, in either cash or common stock at the
election of the director. Directors do not have the right to vote with respect
to any Stock Units. Directors also have the opportunity to defer until
termination of service, or until any date at least five years after the
deferral, all or a portion of their cash fees. Any deferred cash amounts, and
earnings or losses thereon, are recorded in a memorandum account maintained for
each director. The right to receive future payments of Stock Unit accounts and
deferred cash accounts is an unsecured claim against the Company's general
assets. Directors who are employees of the Company do not receive any cash or
Stock Units for their services as directors.
 
                                       14

<PAGE>   19
 
         REPORT OF THE CORPORATE GOVERNANCE AND COMPENSATION COMMITTEE
 
COMPENSATION PROGRAM AND POLICIES
 
     The Company's executive compensation program is administered by the
Corporate Governance and Compensation Committee (the "Committee"). In this
capacity, the Committee reviews compensation levels of elected officers,
evaluates performance, considers management succession and related matters, and
administers the Company's incentive plans, including the Executive Variable
Compensation Plan (the "EVC Plan") and the 1990 Unisys Long-Term Incentive Plan
(the "LTIP").
 
     The Company's executive compensation program is designed to attract and
retain executives responsible for the Company's long-term success, to reward
executives for achieving both financial and strategic company goals, to align
executive and stockholder interests through long-term, equity-based plans, and
to provide a compensation package that recognizes individual contributions as
well as overall business results. As a result, a substantial portion of each
executive's total compensation is intended to be variable and to be tied closely
to the achievement of specific business objectives and corporate financial
goals, as well as the attainment of the executive's individual performance
objectives. The Company's executive compensation program also takes into account
the compensation practices of companies with whom Unisys competes for executive
talent. These companies (the "peer companies") include the principal companies
included in the peer group indices in the Performance Graph on page 17 of this
Proxy Statement and additional companies in various industries.
 
     The three key components of the Company's executive compensation program
for 1998 were base salary, short-term incentive payments, and long-term
incentive awards in the form of stock options. Overall compensation is intended
to be competitive for comparable positions at the peer companies.
 
     The Company's policies with respect to each of the elements of its
executive compensation program, as well as the basis for the compensation
awarded to the chief executive officer, are discussed below.
 
BASE SALARY
 
     Each executive's base salary is initially determined with reference to
competitive pay practices and is dependent upon the executive's level of
responsibility and experience. The Committee uses its discretion, rather than a
formal weighting system, to evaluate these factors and to determine individual
base salary levels. Thereafter, base salaries are reviewed periodically, and
increases are made based on the Committee's subjective assessment of individual
performance, as well as the factors discussed above.
 
SHORT-TERM INCENTIVE PAYMENTS
 
     For 1998, all of the Company's executive officers participated in the EVC
Plan. This plan's stated purpose is to motivate and reward elected officers and
other key executives for the attainment of individual and/or corporate
performance goals. Under the plan, the Committee has the discretion to determine
the conditions (including performance objectives) applicable to annual award
payments and the amounts of such awards. With respect to executives other than
Mr. Weinbach, awards under the plan for 1998 were generally determined as
follows.
 
     Early in 1998, executives were assigned target award amounts for the year,
which were typically stated as a percentage of base salary (ranging, in the case
of elected officers other
 
                                       15

<PAGE>   20
 
than the chief executive officer, from 45% to 60%). Performance goals were also
established based upon the financial performance of Unisys (generally,
achievement of pre-established revenue, profit, and cash flow objectives) and
upon individual performance objectives. Actual award amounts could range from
zero to 150% of target, depending upon the Committee's assessment of the
Company's achievement of its overall global business goals and the individual's
performance, including cooperation in achieving corporate-wide results. In 1998,
the Company met the performance goals established for the year. Awards paid for
1998 reflected these results plus individual accomplishments.
 
LONG-TERM INCENTIVE AWARDS
 
     Under the LTIP, stock options may be granted to the Company's executive
officers and other key employees. The size of stock option awards is based
primarily on the individual's responsibilities with Unisys. The Committee does
not determine the size of such awards by reference to the amount or value of
stock options currently held by an executive officer.
 
     Stock options are designed to align the interests of executives with those
of stockholders. Stock options are granted with an exercise price equal to the
average market price of Unisys Common Stock on the date of grant, and current
grants vest over four years. This approach is designed to encourage the creation
of stockholder value over the long term since no benefit is realized unless the
price of the Common Stock rises over a number of years.
 
COMPENSATION OF THE CHIEF EXECUTIVE OFFICER
 
     Lawrence A. Weinbach became the Company's Chairman, President and Chief
Executive Officer on September 23, 1997. In connection with his employment, the
Company entered into the employment agreement described at page 13. Under the
employment agreement, Mr. Weinbach is entitled to a base salary at the rate of
$1,200,000 per year and, for 1998 and 1999, is guaranteed a minimum annual bonus
equal to 100% of the base salary paid to him in that year. In light of the
Company's strong 1998 financial performance, as well as significant improvements
in customer and employee satisfaction and the Company's reputation in the market
place under Mr. Weinbach's leadership, the Committee awarded Mr. Weinbach a
bonus of $1,800,000, or 150% of base salary, for 1998. In 1998, Mr. Weinbach
also was granted the stock options described on page 11.
 
DEDUCTIBILITY OF EXECUTIVE COMPENSATION
 
     Section 162(m) of the Internal Revenue Code imposes a $1 million annual
limit on the amount of compensation that may be deducted by the Company with
respect to each Named Officer employed as of the last day of the applicable
year. The limitation does not apply to compensation based on the attainment of
objective performance goals. The Committee has considered the impact of the
deduction limitation and has determined that it is not in the best interests of
the Company or its stockholders to base compensation solely on objective
performance criteria. Rather, the Committee believes that it should retain the
flexibility to base compensation on its subjective evaluation of performance as
well as on the attainment of objective goals.
 
Corporate Governance and Compensation Committee
 
     Melvin R. Goodes            Edwin A. Huston           Kenneth A. Macke
 
                                       16

<PAGE>   21
 
 
                           STOCK PERFORMANCE GRAPH
 
     The following graph compares the yearly percentage change in the cumulative
total stockholder return on Unisys Common Stock during the five fiscal years
ended December 31, 1998 with the cumulative total return on the Standard &
Poor's 500 Stock Index, the Standard & Poor's Computers (Hardware) Index and the
Standard & Poor's Computers (Software and Services) Index. The comparison
assumes $100 was invested on December 31, 1993 in Unisys Common Stock and in
each of such indices and assumes reinvestment of dividends.
 
[Unisys Corporation Performance Graph]
 

<TABLE>
<CAPTION>
                                         UNISYS CORPORATION          S&P 500                                    S&P COMPUTERS
                                         ------------------          -------             S&P COMPUTERS           (SOFTWARE &
                                                                                           (HARDWARE)             SERVICES)
                                                                                         -------------          -------------
<S>                                     <C>                    <C>                    <C>                    <C>
'1993'                                         100.00                 100.00                 100.00                 100.00
'1994'                                          68.00                 101.00                 129.00                 118.00
'1995'                                          44.00                 139.00                 172.00                 166.00
'1996'                                          53.00                 171.00                 230.00                 258.00
'1997'                                         110.00                 229.00                 337.00                 360.00
'1998'                                         273.00                 294.00                 590.00                 652.00
</TABLE>

 
                                       17

<PAGE>   22
 
                                GENERAL MATTERS
 
POLICY ON CONFIDENTIAL VOTING
 
     It is the Company's policy that all stockholder proxies, ballots, and
voting materials that identify the vote of a specific stockholder shall, if
requested by that stockholder on such proxy, ballot, or materials, be kept
permanently confidential and shall not be disclosed to the Company, its
affiliates, directors, officers, and employees or to any third parties, except
as may be required by law, to pursue or defend legal proceedings, or to carry
out the purpose of, or as permitted by, the policy. Under the policy, vote
tabulators and inspectors of election are to be independent parties who are
unaffiliated with and are not employees of the Company. The policy provides that
it may, under certain circumstances, be suspended in the event of a proxy
solicitation in opposition to a solicitation of management. The Company may at
any time be informed whether or not a particular stockholder has voted. Comments
written on proxies or ballots, together with the name and address of the
commenting stockholder, will also be made available to the Company.
 
STOCKHOLDER PROPOSALS
 
     The deadline for submitting stockholder proposals to the Company for
inclusion in the proxy materials for the 2000 Annual Meeting of Stockholders is
November 17, 1999.
 
     Any stockholder who intends to present a proposal at the 2000 Annual
Meeting and has not sought to include the proposal in the Company's proxy
materials must give the Company notice of the proposal no later than January 30,
2000.
 
ELECTRONIC ACCESS TO PROXY MATERIALS AND ANNUAL REPORT
 
     This Proxy Statement and the 1998 Annual Report are available on the
Company's Internet site at www.unisys.com/investor/proxy99 and
www.unisys.com/annual/annual98. Most stockholders can elect to view future proxy
statements and annual reports over the Internet instead of receiving paper
copies in the mail and thus can save the Company the cost of producing and
mailing these documents. If you are a stockholder of record, you can choose this
option by completing and submitting the consent form that you will receive for
next year's proxy materials. If you hold your shares through a bank, broker or
other holder of record, check the information provided by that entity for
instructions on how to elect to view future proxy statements and annual reports
over the Internet.
 
OTHER MATTERS
 
     At the date of this Proxy Statement, the Board of Directors knows of no
matter that will be presented for consideration at the Annual Meeting other than
those described in this Proxy Statement. If any other matter properly comes
before the Annual Meeting, the persons appointed as proxies will vote thereon in
their discretion.
 
                                       18

<PAGE>   23
 
     The Company will bear the cost of soliciting proxies. Such cost will
include charges by brokers and other custodians, nominees, and fiduciaries for
forwarding proxies and proxy material to the beneficial owners of Unisys Common
Stock. Solicitation may also be made personally, or by telephone or telegraph,
by the Company's directors, officers, and employees without additional
compensation. In addition, the Company has retained Morrow & Co., Inc. to assist
in the solicitation of proxies for a fee of approximately $9,500, plus expenses.
 
                                          By Order of the Board of Directors,
 
                                          /s/ Harold S. Barron
                                          Harold S. Barron
                                          Senior Vice President,
                                          General Counsel and Secretary
Dated: March 16, 1999
 
                                       19

<PAGE>   24
                               UNISYS CORPORATION
   PLEASE MARK VOTE IN OVAL IN THE FOLLOWING MANNER USING DARK INK ONLY. / /

[                                                                              ]

THE BOARD OF DIRECTORS RECOMMENDS A VOTE FOR ITEMS 1 AND 2.


                                       FOR      WITHHELD         FOR all
                                       all      from all      except as noted

1.   Election of Directors             / /        / /               / /
     Nominees:
     01   J.P. Bolduc
     02   James J. Duderstadt
     03   Kenneth A. Macke


_________________________________________________
     (except nominee(s) written above)


                                                        FOR    AGAINST   ABSTAIN

2. Ratification of Selection of Independent Auditors    / /      / /       / /

                  Mark Here to Have                     / /
                  Your Vote Remain
                  Confidential




         Date:___________________________________, 1999


________________________________________________________
                     (Signature)


________________________________________________________
                     (Signature)


THIS PROXY WILL BE VOTED IN ACCORDANCE WITH SPECIFICATIONS MADE. IF NO CHOICES
ARE INDICATED, THIS PROXY WILL BE VOTED FOR ITEMS 1 AND 2 AND THE TRUSTEE FOR
THE SAVINGS PLAN WILL VOTE AS DESCRIBED ON PAGE 2 OF THE PROXY STATEMENT.

NOTE: Please sign exactly as name appears hereon. For joint accounts both owners
should sign. When signing as executor, administrator, attorney, trustee,
guardian, corporate officer, etc., please give your full title.



              IF YOU WANT TO VOTE BY TELEPHONE OR VIA THE INTERNET,
                       PLEASE READ THE INSTRUCTIONS BELOW.
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CONTROL NUMBER                                                       UNISYS


                          VOTE BY TELEPHONE OR INTERNET

Unisys Corporation encourages you to take advantage of the new and convenient
ways to vote your shares on proposals covered in this year's Proxy Statement.
You may vote by mail or choose one of the two voting methods outlined below to
vote your proxy. This year, voting has been made easier than ever.


VOTE BY TELEPHONE  There is NO CHARGE for this call. On a touch-tone telephone,
                   call TOLL FREE 888-514-5365 to vote your proxy - 24 hours a
                   day, 7 days a week. You will need to have the above proxy
                   card in hand when you call. Please enter the Control Number
                   located in the box in the upper left corner of this voting
                   form.

                   1.  To vote as the Board of Directors recommends on both
                       proposals, press 1. Your vote will be confirmed and cast
                       as you directed, then the call will end. If you wish to
                       cast a separate vote on each proposal, press 0.

                   2.  If you select 0 to vote on each proposal separately, you
                       will hear these instructions: 

                       PROPOSAL 1 - To vote FOR all nominees, press 1; to
                       WITHHOLD from all nominees, press 9; to WITHHOLD from AN
                       INDIVIDUAL nominee, press 0 and enter the two-digit
                       number that appears on the above proxy card next to the
                       name of the nominee you DO NOT wish to vote for. Once
                       you have completed voting for the Directors, press 0. 

                       PROPOSAL 2 - To vote FOR, press 1; to vote AGAINST, press
                       9; to ABSTAIN, press 0. Your vote selection will be
                       repeated and you will have an opportunity to confirm it.


VOTE BY INTERNET   Vote on the Internet 24 hours a day, 7 days a week. Here is
                   the address:

                   www.harrisbank.com/wproxy. 

                   Have this voting form in hand when you access the website.
                   Then follow the instructions that are provided.


   IF YOU VOTE BY TELEPHONE OR THE INTERNET, DO NOT MAIL BACK THIS VOTING FORM.

<PAGE>   25
                               UNISYS CORPORATION
               PROXY FOR ANNUAL MEETING TO BE HELD APRIL 29, 1999
           THIS PROXY IS SOLICITED ON BEHALF OF THE BOARD OF DIRECTORS


  THE UNDERSIGNED HEREBY APPOINTS MELVIN R. GOODES, KENNETH A. MACKE AND
  LAWRENCE A. WEINBACH, AND EACH OF THEM, PROXIES, WITH POWER OF SUBSTITUTION,
  TO VOTE ALL SHARES OF COMMON STOCK WHICH THE UNDERSIGNED IS ENTITLED TO VOTE
  AT THE 1999 ANNUAL MEETING OF STOCKHOLDERS OF UNISYS CORPORATION, AND AT ANY
  ADJOURNMENT THEREOF, AS DIRECTED ON THE REVERSE SIDE HEREOF WITH RESPECT TO
  THE ITEMS SET FORTH IN THE ACCOMPANYING PROXY STATEMENT AND IN THEIR
  DISCRETION UPON SUCH OTHER MATTERS AS MAY PROPERLY COME BEFORE THE MEETING.
  THIS CARD ALSO PROVIDES VOTING INSTRUCTIONS (FOR SHARES CREDITED TO THE
  ACCOUNT OF THE UNDERSIGNED, IF ANY) TO THE TRUSTEE FOR THE UNISYS SAVINGS PLAN
  (THE "SAVINGS PLAN") AS MORE FULLY DESCRIBED ON PAGE 2 OF THE PROXY STATEMENT.

       IF YOU ARE VOTING BY MAIL, PLEASE MARK, DATE, SIGN AND RETURN THIS
             PROXY/VOTING INSTRUCTION CARD IN THE ENCLOSED ENVELOPE

                  (CONTINUED AND TO BE SIGNED ON REVERSE SIDE.)



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