HALLIBURTON CO
DEF 14A, 1999-04-05
HEAVY CONSTRUCTION OTHER THAN BLDG CONST - CONTRACTORS
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<PAGE>
 
                          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 (S) 240.14a-11(c) or (S) 240.14a-12

                              Halliburton Company
- --------------------------------------------------------------------------------
               (Name of Registrant as Specified In Its Charter)

                                      N/A
- --------------------------------------------------------------------------------
   (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.:

     -------------------------------------------------------------------------


     (3) Filing Party:
      
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     (4) Date Filed:

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Notes:

<PAGE>
 
                         [LOGO OF HALLIBURTON COMPANY]
 
                                                                 March 25, 1999
 
To Our Stockholders:
 
  You are cordially invited to attend the Annual Meeting of Stockholders of
Halliburton Company which will be held on Tuesday, May 18, 1999, at 9:00 a.m.
in the Horchow Auditorium of the Dallas Museum of Art, 1717 North Harwood
Street, Dallas, Texas 75201.
 
  At the meeting, as set forth in the accompanying Notice of Annual Meeting
and Proxy Statement, stockholders are being asked to elect a Board of
Directors of fourteen Directors to serve for the coming year and to ratify the
selection of Arthur Andersen LLP as independent accountants to examine the
financial statements and books and records of the Company for 1999.
 
  It is very important that your shares are represented and voted at the
meeting. Accordingly, please sign, date and return the enclosed proxy card or
call the toll-free number indicated in the enclosed telephone voting
instructions. If you attend the meeting, you may vote in person even if you
have previously mailed a proxy card or voted by telephone. We would appreciate
your informing us on the proxy card if you expect to attend the meeting so
that we can provide adequate seating.
 
  The continuing interest of our stockholders in the business of the Company
is appreciated and we hope many of you will be able to attend the Annual
Meeting.
 
  Sincerely,
 

/s/ WILLIAM E. BRADFORD          /s/ DICK CHENEY

    William E. Bradford              Dick Cheney
    Chairman of the Board            Chief Executive Officer


<PAGE>
 
                         [LOGO OF HALLIBURTON COMPANY]
 
                   Notice of Annual Meeting of Stockholders
 
                            to be Held May 18, 1999
 
  The Annual Meeting of Stockholders of HALLIBURTON COMPANY, a Delaware
corporation (the "Company"), will be held on Tuesday, May 18, 1999, at 9:00
a.m., in the Horchow Auditorium of the Dallas Museum of Art, 1717 North
Harwood Street, Dallas, Texas 75201, to consider and act upon the matters
discussed in the attached Proxy Statement as follows:
 
  1. To elect fourteen (14) Directors to serve for the ensuing year and until
     their successors shall be elected and shall qualify.
 
  2. To consider and act upon a proposal to ratify the appointment of Arthur
     Andersen LLP as independent accountants to examine the financial
     statements and books and records of the Company for the year 1999.
 
  3. To transact such other business as may properly come before the meeting
     or any adjournment or adjournments thereof.
 
  The Board of Directors has fixed Monday, March 22, 1999, at the close of
business, as the record date for the determination of stockholders entitled to
notice of and to vote at the meeting and at any adjournment thereof. A Proxy
Statement is attached and incorporated herein by reference.
 
                                           By order of the Board of Directors,
 
                                                   /s/ SUSAN S. KEITH
 
                                                     Susan S. Keith
                                              Vice President and Secretary
 
March 25, 1999
 
                               ----------------
 
  Stockholders are urged to vote their shares as promptly as possible by
either (1) signing, dating and returning the enclosed proxy card or (2)
calling the toll-free number indicated in the enclosed telephone voting
instructions.
<PAGE>
 
                                PROXY STATEMENT
 
                              GENERAL INFORMATION
 
  The accompanying proxy is solicited by and on behalf of the Board of
Directors of Halliburton Company (the "Company"). By executing and returning
the enclosed proxy or by following the enclosed telephone voting instructions,
you authorize the persons named in the proxy to represent you and vote your
shares in connection with the matters set forth in the Notice of Annual
Meeting.
 
  If you attend the meeting, you may, of course, vote in person. But, if you
are not present, your shares can be voted only if you have returned a properly
executed proxy or followed the telephone voting instructions. If you have
returned a properly executed proxy or followed the telephone voting
instructions, the related shares will be voted as you specify. If no
specification is made, the shares will be voted in accordance with the
recommendations of the Board of Directors. You may revoke the authorization
given in your proxy or telephone call at any time before the shares are voted
at the meeting.
 
  The record date for determination of the stockholders entitled to vote at
the Annual Meeting is the close of business on March 22, 1999. The Company's
Common Stock, par value $2.50, is the only class of capital stock of the
Company that is outstanding. As of March 22, 1999, there were 440,337,421
shares of Common Stock outstanding. Each of the outstanding shares of Common
Stock is entitled to one vote on each matter submitted to the stockholders for
a vote at the meeting. A complete list of stockholders entitled to vote will
be kept at the Company's offices at the address specified below for ten days
prior to the Annual Meeting.
 
  Votes cast by written proxy, telephone or in person at the Annual Meeting
will be counted by the persons appointed by the Company to act as election
inspectors for the meeting. Except as set forth below, the affirmative vote of
the majority of shares present in person or represented by proxy at the
meeting and entitled to vote on the subject matter shall be the act of the
stockholders. Shares for which a holder has elected to abstain on a matter
will count for purposes of determining the presence of a quorum and for
purposes of determining the outcome of such matter.
 
  In the election of Directors, the candidates for election receiving the
highest number of affirmative votes of the shares entitled to be voted for
them (whether or not a majority of the shares present), up to the number of
Directors to be elected by those shares, will be elected; shares present but
not voting will be disregarded (except for quorum purposes) and will have no
legal effect.
 
  The election inspectors will treat shares referred to as "broker non-votes"
(i.e., shares held in street name which cannot be voted by a broker on certain
matters in the absence of instructions from the beneficial owner of the
shares) as shares that are present and entitled to vote for purposes of
determining the presence of a quorum. For purposes of determining the outcome
of any matter as to which the broker has indicated in writing on the proxy
that it does not have discretionary authority to vote, however, such shares
will be treated as not present and not entitled to vote with respect to that
matter (even though those shares may be entitled to vote on other matters).
 
  In accordance with the Company's confidential voting policy, no vote of any
stockholder, whether by written proxy, telephone or in person, will be
disclosed to the officers, Directors or employees of the Company, except (i)
as necessary to meet applicable legal requirements and to assert claims for
and defend claims against the Company, (ii) when disclosure is voluntarily
made or requested by the stockholder, (iii) when stockholders write comments
on proxy cards, or (iv) in the event of a proxy solicitation not approved and
recommended by the Board of Directors. The proxy solicitor, the election
inspectors and the tabulators of all proxies, ballots and voting tabulations
that identify stockholders are independent and are not employees of the
Company.
 
  This Proxy Statement, form of proxy and telephone voting instructions are
being sent to stockholders on or about April 5, 1999. The Company's Annual
Report to Stockholders, including financial statements, for the fiscal year
ended December 31, 1998 accompanies this Proxy Statement. Such Annual Report
is not to be considered as a part of the proxy solicitation material or as
having been incorporated herein by reference.
 
  The principal executive offices of the Company are located at 3600 Lincoln
Plaza, 500 N. Akard Street, Dallas, Texas 75201-3391.
 
                                       1
<PAGE>
 
                             ELECTION OF DIRECTORS
 
                                   (Item 1)
 
  Effective as of the consummation of the merger with Dresser Industries, Inc.
(the "Dresser Merger") on September 29, 1998 (the "Effective Date"), the
number of Directors constituting the Board of Directors of the Company was
increased from 10 to 14 and Messrs. William E. Bradford, Lawrence S.
Eagleburger, Ray L. Hunt, J. Landis Martin and Jay A. Precourt were elected as
Directors. Mr. Dale P. Jones, who served as a Director since 1988, retired
from the Board of Directors as of the Effective Date.
 
  Fourteen Directors are to be elected to serve for the ensuing year and until
their successors are elected and qualify. All of the fourteen nominees
hereinafter named are presently Directors of the Company. It is intended that
the Common Stock represented by the proxies, in the absence of instructions to
the contrary, will be voted for the election as Directors of the fourteen
nominees or, if any such nominee shall be unwilling or unable to serve,
favorable and uninstructed proxies will be voted for a substitute nominee
designated by the Board of Directors, unless the Board of Directors, because
of the unavailability of a suitable substitute, reduces the number of
Directors to be elected. Each nominee has indicated approval of his or her
nomination and his or her willingness to serve if elected.
 
Information With Respect to Nominees for Director
 
                ANNE L. ARMSTRONG, 71, Regent, Texas A&M University System;
              Member, Board of Trustees, Center for Strategic and
              International Studies; Member, National Security Advisory Board,
              Department of Defense; former Chairman of the President's
              Foreign Intelligence Advisory Board, 1981-1990; former
              Ambassador to Great Britain; joined Halliburton Company Board in
              1977; Chairman of the Health, Safety and Environment Committee
              and member of the Management Oversight and the Nominating and
              Corporate Governance Committees; Director of American Express
              Company and Boise Cascade Corporation.
[PHOTO OF ARMSTRONG]
 
                WILLIAM E. BRADFORD, 64, Chairman of the Board of the Company;
              Chairman of the Board of Dresser Industries, Inc., 1996-1998;
              Chief Executive Officer of Dresser Industries, Inc., 1995-1998;
              President of Dresser Industries, Inc., 1992-1996; Chief
              Operating Officer of Dresser Industries, Inc., 1992-1995;
              President and Chief Executive Officer of Dresser-Rand Company, a
              51% joint venture partnership, 1988-1992; Senior Vice President-
              Operations of Dresser Industries, Inc., 1984-1992; joined
              Halliburton Company Board in 1998; Director of Ultramar Diamond
              Shamrock Corporation and Kerr-McGee Corporation.
[PHOTO OF BRADFORD]
 
                RICHARD B. (DICK) CHENEY, 58, Chief Executive Officer of the
              Company; Chairman of the Board and Chief Executive Officer of
              the Company, 1997-1998; Chairman of the Board, President and
              Chief Executive Officer of the Company, 1996-1997; President and
              Chief Executive Officer of the Company, 1995; Senior Fellow,
              American Enterprise Institute for Public Policy Research, 1993-
              1995; United States Secretary of Defense, 1989-1993; Member,
              United States House of Representatives, 1979-1989; joined
              Halliburton Company Board in 1995; Director of Union Pacific
              Corporation, The Procter & Gamble Company and Electronic Data
              Systems Corporation; Member of the Board of Trustees, American
              Enterprise Institute for Public Policy Research.
[PHOTO OF CHENEY]
 
                                       2
<PAGE>
 
                LORD CLITHEROE, 69, Chairman, The Yorkshire Bank, PLC; Deputy
              Chief Executive, The RTZ Corporation PLC, 1987-1989; Executive
              Director, The RTZ Corporation PLC, 1968-1987; joined Halliburton
              Company Board in 1987; Chairman of the Management Oversight
              Committee and member of the Health, Safety and Environment and
              the Nominating and Corporate Governance Committees.
[PHOTO OF CLITHEROE]
 
                ROBERT L. CRANDALL, 63, Chairman Emeritus, AMR
              Corporation/American Airlines, Inc. (engaged primarily in the
              air transportation business); Chairman, President and Chief
              Executive Officer, AMR Corporation and Chairman and Chief
              Executive Officer, American Airlines, Inc. 1985-1998; President,
              American Airlines, Inc., 1985-1995; joined Halliburton Company
              Board in 1986; Chairman of the Audit Committee and member of the
              Compensation and the Management Oversight Committees; Director
              of MediaOne Group, Inc. and Director and non-executive Chairman
              of Celestica, Inc.
[PHOTO OF CRANDALL]
 
                CHARLES J. DIBONA, 67, President and Chief Executive Officer
              (retired), American Petroleum Institute (a major petroleum
              industry trade association), 1979-1997; joined Halliburton
              Company Board in 1997; member of the Health, Safety and
              Environment, the Nominating and Corporate Governance and the
              Management Oversight Committees; Chairman of the Board of
              Trustees, Logistics Management Institute.
[PHOTO OF DIBONA]
 
                LAWRENCE S. EAGLEBURGER, 68, Senior Foreign Policy Advisor,
              Baker, Donelson, Bearman & Caldwell (a Washington, D.C. law
              firm); Chairman, International Commission on Holocaust Era
              Insurance Claims; United States Secretary of State, Department
              of State, 1992-1993; Acting Secretary of State, 1992; Deputy
              Secretary of State, 1989-1992; joined Halliburton Company Board
              in 1998; member of the Management Oversight and the Nominating
              and Corporate Governance Committees; Director of Phillips
              Petroleum Company, Stimsonite, Universal Corporation and COMSAT.
[PHOTO OF EAGLEBURGER]
 
                W. R. HOWELL, 63, Chairman Emeritus, J.C. Penney Company, Inc.
              (a major retailer); Chairman of the Board, J.C. Penney Company,
              Inc., 1983-1996; Chief Executive Officer, J.C. Penney Company,
              Inc., 1983-1995; joined Halliburton Company Board in 1991;
              Chairman of the Compensation Committee and member of the
              Management Oversight and the Audit Committees; Director of Exxon
              Corporation, Warner-Lambert Company, Bankers Trust Company,
              Bankers Trust New York Corporation, The Williams Companies, Inc.
              and Central and South West Corporation.
[PHOTO OF HOWELL]
 
                RAY L. HUNT, 55, For more than five years, Chairman of the
              Board and Chief Executive Officer, Hunt Oil Company (oil and gas
              exploration and development); Chairman of the Board, Chief
              Executive Officer and President, Hunt Consolidated, Inc. and
              Chairman of the Board, Chief Executive Officer and President,
              RRH Corporation; joined Halliburton Company Board in 1998;
              member of the Compensation and the Management Oversight
              Committees; Director of Electronic Data Systems Corporation,
              PepsiCo, Inc., Ergo Science Incorporated, Security Capital Group
              Incorporated and Federal Reserve Bank of Dallas.
[PHOTO OF HUNT]
 
                DELANO E. LEWIS, 60, President and Chief Executive Officer
              (retired), National Public Radio (produces and distributes
              original programming and provides support to member stations),
              1994-1998; President and Chief Executive Officer, C&P Telephone
              Company, a subsidiary of Bell Atlantic Corporation, 1990-1993;
              joined Halliburton Company Board in 1996; member of the
              Compensation, the Health, Safety and Environment and the
              Management Oversight Committees; Director of Colgate-Palmolive
              Company, Eastman Kodak Company, BET Holdings, Inc. and the
              Poynter Institute.
[PHOTO OF LEWIS]
 
                                       3
<PAGE>
 
                J. LANDIS MARTIN, 53, For more than five years, President and
              Chief Executive Officer, NL Industries, Inc. (a manufacturer and
              marketer of titanium dioxide pigments) and Chairman, Titanium
              Metals Corporation (an integrated producer of titanium metals);
              Chief Executive Officer, Titanium Metals Corporation, since
              1995; Chairman of the Board and Chief Executive Officer, Baroid
              Corporation (and its predecessor), acquired by Dresser
              Industries, Inc. in 1994, 1990-1994; joined Halliburton Company
              Board in 1998; member of the Audit and the Management Oversight
              Committees; Director of NL Industries, Inc., Titanium Metals
              Corporation, Tremont Corporation and Apartment Investment and
              Management Corporation.
[PHOTO OF MARTIN]
 
                JAY A. PRECOURT, 61, Chairman of the Board, Wyoming Refining
              Company; Vice Chairman and Chief Executive Officer, Tejas Gas
              Corporation, 1986-1999; President, Tejas Gas Corporation, 1996-
              1998; joined Halliburton Company Board in 1998; member of the
              Health, Safety and Environment and the Management Oversight
              Committees; Chairman of the Board of Founders Funds, Inc. and
              Director of the Timken Company.
 
[PHOTO OF PRECOURT]
                C. J. SILAS, 66, Chairman of the Board and Chief Executive
              Officer (retired), Phillips Petroleum Company (engaged in
              exploration and production of crude oil, natural gas and natural
              gas liquids on a worldwide basis, the manufacture of plastics
              and petrochemicals and other activities), 1985-1994; joined
              Halliburton Company Board in 1993; member of the Compensation,
              the Audit and the Management Oversight Committees; Director of
              Reader's Digest Association, Inc.
 
[PHOTO OF SILAS]
                RICHARD J. STEGEMEIER, 70, Chairman Emeritus, Unocal
              Corporation (an integrated petroleum company); Chairman of the
              Board, Unocal Corporation, 1989-1995; Chief Executive Officer,
              Unocal Corporation, 1988-1994; President, Unocal Corporation,
              1985-1992; Chief Operating Officer, Unocal Corporation, 1985-
              1988; joined Halliburton Company Board in 1994; Chairman of the
              Nominating and Corporate Governance Committee and member of the
              Audit and the Management Oversight Committees; Director of
              Foundation Health Systems, Inc., Northrop Grumman Corporation,
              Sempra Energy and Montgomery Watson, Inc.
[PHOTO OF STEGEMEIER]
 
                                       4
<PAGE>
 
Stock Ownership of Certain Beneficial Owners and Management
 
  The following table sets forth information with respect to persons or groups
who, to the Company's knowledge (based on information contained in Schedules
13G filed with the Securities and Exchange Commission with respect to
beneficial ownership at December 31, 1998), own or have the right to acquire
more than five percent of the Common Stock of the Company.
<TABLE>
<CAPTION>
                                                          Amount and
                                                          Nature of     Percent
  Name and Address                                        Beneficial      of
  of Beneficial Owner                                     Ownership      Class
  -------------------                                     ----------    -------
<S>                                                       <C>           <C>
FMR Corp. ............................................... 46,213,273(1) 10.511%
 82 Devonshire Street
 Boston, MA 02109
Barrow, Hanley, Mewhinney & Strauss, Inc. ............... 22,045,960(2)   5.00%
 One McKinney Plaza
 3232 McKinney Avenue, 15th Floor
 Dallas, TX 75204-2429
</TABLE>
- --------
(1) The number of shares reported includes 40,906,307 shares beneficially
    owned by Fidelity Management & Research Company, 4,628,866 shares owned by
    Fidelity Management Trust Company and 678,100 shares held by Fidelity
    International Limited. FMR Corp., through control of Fidelity Management &
    Research Company and Fidelity Management Trust Company, has sole
    dispositive power over the shares with the exception of those held
    beneficially by Fidelity International Limited. FMR Corp. has sole power
    to vote or to direct the vote of 3,193,666 shares of Common Stock.
(2) Barrow, Hanley, Mewhinney & Strauss, Inc. has sole power to dispose of all
    such shares, sole power to vote or to direct the vote of 4,169,700 shares
    and shared power to vote or direct the vote of 17,876,260 shares.
 
                                       5
<PAGE>
 
  The following table sets forth, as of March 22, 1999, the amount of Company
Common Stock owned beneficially by each Director and nominee for Director,
each of the executive officers named in the Summary Compensation Table on page
19 and all Directors, nominees for Director and executive officers as a group.
 
<TABLE>
<CAPTION>
                                                    Amount and Nature of
                                                    Beneficial Ownership
                                               --------------------------------
                                                             Shared
                                               Sole Voting Voting or
 Name of Beneficial Owner or                   and Invest- Investment  Percent
 Number of Persons in Group                    ment Power   Power(1)   of Class
 ---------------------------                   ----------- ----------  --------
<S>                                            <C>         <C>         <C>
Anne L. Armstrong.............................      4,400                  *
William E. Bradford(3)........................    472,033                  *
Richard B. Cheney(3)..........................    969,667                  *
Lord Clitheroe................................      3,000                  *
Lester L. Coleman(3)..........................    177,104                  *
Robert L. Crandall............................      3,400                  *
Charles J. DiBona.............................        400                  *
Lawrence S. Eagleburger(3)....................      9,756                  *
W. R. Howell..................................      2,300                  *
Ray L. Hunt(3)................................     70,446    52,284(2)     *
Dale P. Jones (3).............................    396,102                  *
David J. Lesar(3).............................    391,782                  *
Ken R. LeSuer(3)..............................    379,228     3,772(2)     *
Delano E. Lewis...............................      1,500                  *
J. Landis Martin(3)...........................     91,145                  *
Jay A. Precourt(3)............................      7,809                  *
C. J. Silas...................................      2,400                  *
Richard J. Stegemeier.........................      2,000     2,000(2)     *
Donald C. Vaughn(3)...........................    193,527                  *
Shares owned by all current Directors,
 nominees for Director and
 executive officers as a group (25
 persons)(3)..................................  3,640,797    58,056        *
</TABLE>
- --------
 * Less than 1% of shares outstanding.
(1) The Halliburton Stock Fund, an investment fund established under the
    Halliburton Company Employee Benefit Master Trust to hold Company Common
    Stock for certain of the Company's profit sharing, retirement and savings
    plans (the "Plans"), held 3,286,282 shares of Company Common Stock at
    March 12, 1999. Two executive officers not named in the above table have
    beneficial interests in the Halliburton Stock Fund. Shares of Company
    Common Stock held in the Halliburton Stock Fund are not allocated to any
    individual's account and an aggregate 2,218 shares which might be deemed
    to be beneficially owned as of March 12, 1999 by such unnamed executive
    officers are not included in the table above. Shares held in the
    Halliburton Stock Fund are voted by the Trustee, State Street Bank and
    Trust Company, in accordance with voting instructions from the
    participants. Under the terms of the Plans, a participant has the right,
    from time to time, to determine whether up to 15% of his account is
    invested in the Halliburton Stock Fund or in alternative investments
    permitted by the Plans. The Trustee, however, determines when sales or
    purchases are to be made.
    Mr. Martin has a beneficial interest in the NL Industries, Inc. Savings
    Plan. Shares of Company Common Stock held by that plan are not allocated to
    any individual's account and, accordingly, 2,373 shares which might be
    deemed to be beneficially owned by Mr. Martin as of February 18, 1999 are
    not included in the above table.
(2) Mr. Hunt holds 52,284 shares as the trustee of trusts established for the
    benefit of his children. Mr. Hunt disclaims beneficial ownership of 17,428
    shares owned by another trust established for one of his children as to
    which he is not the trustee. 3,772 shares are held in joint tenancy by Mr.
    LeSuer and his wife. Mr. LeSuer and his wife share voting and investment
    power with respect to such shares. Mr. Stegemeier and his wife hold 2,000
    shares as co-trustees of a family trust and share voting and investment
    power with respect to such shares.
(3) Included in the table are shares of Common Stock that may be purchased
    pursuant to outstanding stock options (and, in the case of Messrs.
    Bradford and Vaughn, related restricted incentive stock awards under
    certain Dresser Industries, Inc. stock compensation plans) within 60 days
    of the date hereof for the following: Mr. Bradford-270,605; Mr. Cheney-
    726,667; Mr. Coleman-139,334; Mr. Eagleburger-499; Mr. Hunt-499; Mr.
    Jones-320,002; Mr. Lesar-185,336; Mr. LeSuer-303,001; Mr. Martin-499; Mr.
    Precourt-499; Mr. Vaughn-112,429 and five unnamed executive officers-
    282,168. Until such time as the options are exercised, the aforesaid
    individuals will neither have voting nor investment power with respect to
    the underlying shares of Common Stock but only have the right to acquire
    beneficial ownership thereof through exercise of their respective options.
 
                                       6
<PAGE>
 
                             CORPORATE GOVERNANCE
 
  The Board of Directors believes that the primary responsibility of Directors
is to provide effective governance over the Company's affairs for the benefit
of its stockholders. That responsibility includes:
 
  .  Evaluating the performance of the Chief Executive Officer and taking
     appropriate action, including removal, when warranted;
 
  .  Selecting, evaluating and fixing the compensation of senior management
     of the Company and establishing policies regarding the compensation of
     other members of management;
 
  .  Reviewing succession plans and management development programs for
     members of senior management;
 
  .  Reviewing and approving periodically long-term strategic and business
     plans and monitoring corporate performance against such plans;
 
  .  Adopting policies of corporate conduct, including compliance with
     applicable laws and regulations and maintenance of accounting, financial
     and other controls, and reviewing the adequacy of compliance systems and
     controls;
 
  .  Evaluating periodically the overall effectiveness of the Board; and
 
  .  Deciding on matters of corporate governance.
 
  In 1997, the Board adopted Guidelines to assist it in the exercise of its
responsibilities. Effective as of the Dresser Merger, the Guidelines were
revised as set forth below in order to reflect the management and
organizational changes resulting therefrom. These Guidelines are in addition
to and are not intended to change or interpret any Federal or state law or
regulation, including the Delaware General Corporation Law, or the Certificate
of Incorporation or By-laws of the Company. The Guidelines are subject to
modification from time to time by the Board of Directors.
 
                           Guidelines on Governance
                      (Revised as of September 29, 1998)
 
Operation of The Board; Meetings
 
  1. Chairman of the Board; Chief Executive Officer. The Board believes that,
under normal circumstances, the Chief Executive Officer of the Company should
also serve as the Chairman of the Board. However, given the current
circumstances of the strategic combination of the Company and Dresser
Industries, Inc. and the need to integrate the two companies' businesses, the
Board believes it is in the best interests of the Company at the present time
for the positions of Chief Executive Officer and Chairman of the Board to be
split and for the office of Chairman of the Board to be held by the former
Chairman and Chief Executive Officer of Dresser. The Chief Executive Officer
is responsible to the Board for the overall management and functioning of the
Company. The Chairman of the Board will preside at meetings of the Board of
Directors and stockholders and have such other duties as may be prescribed,
from time to time, by the Board of Directors.
 
  The Chairman of the Management Oversight Committee, which is composed of all
of the outside Directors, will function as the lead director when such
Committee meets in executive session outside the presence of the Chief
Executive Officer and other Company personnel and will serve as the interface
between that Committee and the Chief Executive Officer in communicating the
matters discussed during the executive sessions.
 
  2. Executive Sessions of Outside Directors. The Management Oversight
Committee is composed of all of the outside Directors and meets in executive
session outside the presence of the Chief Executive Officer and other Company
personnel during a portion of each of its five regular meetings per year. In
addition, any member of the Management Oversight Committee may request the
Committee Chairman to call an executive session of such Committee at any time.
 
                                       7
<PAGE>
 
  Each December, the Management Oversight Committee will meet in executive
session to evaluate the performance of the Chief Executive Officer. In
evaluating the Chief Executive Officer, such Committee takes into
consideration the executive's performance in both qualitative and quantitative
areas, such as: leadership and vision; integrity; keeping the Board informed
on matters affecting the Company and its operating units; performance of the
business (including such measurements as total shareholder return and
achievement of financial objectives and goals); development and implementation
of initiatives to provide long-term economic benefit to the Company;
accomplishment of strategic objectives and development of management. The
evaluation will be communicated to the Chief Executive Officer by the Chairman
of the Management Oversight Committee and will be used by the Compensation
Committee in the course of its deliberations when considering the Chief
Executive Officer's compensation for the ensuing year.
 
  3. Regular Attendance of Non-Directors at Board Meetings. The Chief
Financial Officer and the General Counsel will be present at all times during
Board meetings, except where there is a specific reason for one or both of
them to be excluded. In addition, the Chairman of the Board may invite one or
more members of management to be in regular attendance at Board meetings and
may include other officers and employees from time to time as appropriate to
the circumstances.
 
  4. Frequency of Board Meetings. The Board has five regularly scheduled
meetings per year. Special meetings are called as necessary. It is the
responsibility of the Directors to attend the meetings.
 
  Long-term strategic and business plans will be reviewed annually at one of
the Board's regularly scheduled meetings.
 
  5. Board Access to Senior Management. Directors have open access to the
Company's management, subject to reasonable time constraints. In addition,
senior management of the Company routinely attend Board and Committee meetings
and they and other managers frequently brief the Board and the Committees on
particular topics. The Board encourages senior management to bring managers
into Board or Committee meetings and other scheduled events who (a) can
provide additional insight into matters being considered or (b) represent
managers with future potential whom senior management believe should be given
exposure to the members of the Board.
 
  6. Selection of Agenda Items for Board Meetings. The Chairman of the Board
and the Chief Executive Officer jointly establish the agenda for each Board
meeting, although other Board members are free to suggest items for inclusion
on the agenda. Each Director is free to raise at any Board meeting subjects
that are not on the agenda for that meeting.
 
  7. Board/Committee Forward Agenda. A forward agenda of matters requiring
recurring and focused attention by the Board and each Committee will be
prepared and distributed prior to the beginning of each calendar year in order
to ensure that all required actions are taken in a timely manner and are given
adequate consideration.
 
  8. Information Flow; Pre-meeting Materials. In advance of each Board or
Committee meeting, a proposed agenda will be distributed to each member. In
addition, to the extent feasible or appropriate, information and data
important to the members' understanding of the matters to be considered,
including background summaries of presentations to be made at the meeting,
will be distributed prior to the meeting. Directors also routinely receive
monthly financial statements, earnings reports, press releases, analyst
reports and other information designed to keep them informed of the material
aspects of the Company's business, performance and prospects.
 
Board Structure
 
  1. Majority of the Members of the Board Must Be Independent Directors. The
Board believes that as a matter of policy a majority of the members of the
Board should be independent Directors. A Director will be considered
independent if he or she: (a) has not been employed by the Company or an
affiliate in an executive
 
                                       8
<PAGE>
 
capacity; (b) is not, and is not an employee of a company or firm that is, a
significant* advisor or consultant to the Company or its affiliates; (c) is
not an employee or beneficial owner of more than 10% of a significant*
customer or supplier of the Company or its affiliates; (d) does not have a
significant* personal services contract(s) with the Company or its affiliates;
(e) is not affiliated as an employee with a tax-exempt entity that receives
significant contributions from the Company or its affiliates; (f) is not a
spouse, parent, sibling or child of an officer or former officer of the
Company or one of its affiliates; and (g) is not part of an interlocking
directorate in which the Chief Executive Officer or another executive officer
of the Company serves on the board of another corporation that employs the
Director. (* "Significant" means a business relationship which would be
required to be disclosed under SEC rules.)
 
  The definition of independence and compliance with the foregoing policy will
be reviewed periodically by the Nominating and Corporate Governance Committee.
 
  Furthermore, the Board believes that employee Directors should number not
more than two. While such number is not an absolute limitation, other than
with respect to the Chief Executive Officer, who should at all times be a
member of the Board, employee Directors should be limited only to those
officers whose positions or potential make it appropriate for them to sit on
the Board.
 
  2. Size of the Board. The Board currently has 14 members. The By-laws
prescribe that the number of Directors will not be less than eight nor more
than 20.
 
  3. Service of Former Chief Executive Officers and Other Former Employees on
the Board. Employee Directors shall retire from the Board at the time of their
retirement as an employee unless continued service as a Director is requested
and approved by the Board.
 
  4. Annual Election of All Directors. As provided in the Company's By-laws,
all Directors are elected annually.
 
  5. Board Membership Criteria. Candidates nominated for election or
reelection to the Board of Directors should possess the following
qualifications:
 
 .  Personal characteristics:
 
  .  highest personal and professional ethics, integrity and values;
  .  an inquiring and independent mind; and
  .  practical wisdom and mature judgment.
 
 .  Broad training and experience at the policy-making level in business,
   government, education or technology.
 
 .  Expertise that is useful to the Company and complementary to the background
   and experience of other Board members, so that an optimum balance of
   members on the Board can be achieved and maintained.
 
 .  Willingness to devote the required amount of time to carrying out the
   duties and responsibilities of Board membership.
 
 .  Commitment to serve on the Board over a period of several years to develop
   knowledge about the Company's principal operations.
 
 .  Willingness to represent the best interests of all stockholders and
   objectively appraise management performance.
 
 .  Involvement only in activities or interests that do not create a conflict
   with the Director's responsibilities to the Company and its stockholders.
 
  The Nominating and Corporate Governance Committee is responsible for
assessing the appropriate mix of skills and characteristics required of Board
members in the context of the perceived needs of the Board at a given
 
                                       9
<PAGE>
 
point in time and shall periodically review and update the criteria as deemed
necessary. Diversity in personal background, race, gender, age and nationality
for the Board as a whole may be taken into account in considering individual
candidates.
 
  The Nominating and Corporate Governance Committee will evaluate the
qualifications of each Director candidate against the foregoing criteria in
connection with its recommendation to the Board concerning his or her
nomination for election or reelection as a Director.
 
  6. Selection of Directors. The Board is responsible for nominating members
to the Board and for filling vacancies on the Board that may occur between
annual meetings of stockholders. The Nominating and Corporate Governance
Committee, with direct input from the Chief Executive Officer and other Board
members, is responsible for identifying and screening candidates for Board
membership.
 
  7. Director Retirement. The Nominating and Corporate Governance Committee,
in consultation with the Chief Executive Officer, will review each Director's
continuation on the Board annually in connection with its recommendation to
the Board concerning his or her nomination for election or reelection as a
Director.
 
  It is the policy of the Board that each non-employee Director shall retire
from the Board immediately prior to the annual meeting of stockholders
following his or her seventy-second birthday. Employee Directors shall retire
at the time of their retirement from employment with the Company unless
continued service as a Director is approved by the Board.
 
  8. Director Compensation Review. It is appropriate for senior management of
the Company to report periodically to the Compensation Committee on the status
of the Company's Director compensation practices in relation to other
companies of comparable size and the Company's competitors.
 
  Changes in Director compensation, if any, should come upon the
recommendation of the Compensation Committee, but with full discussion and
concurrence by the Board.
 
  9. Conflicts of Interest. If an actual or potential conflict of interest
develops because of a change in the business operations of the Company or a
subsidiary, or in a Director's circumstances (for example, significant and
ongoing competition between the Company and a business with which the Director
is affiliated), the Director should report such matter immediately to the
Chairman of the Board for evaluation. A significant conflict must be resolved
or the Director should resign.
 
  If a Director has a personal interest in a matter before the Board, the
Director shall disclose the interest to the full Board and excuse himself or
herself from participation in the discussion and shall not vote on the matter.
 
Committees of the Board
 
  1. Number and Types of Committees. A substantial portion of the analysis and
work of the Board is done by standing Board Committees. A Director is expected
to participate actively in the meetings of each Committee to which he or she
is appointed.
 
  The Board has established the following standing Committees: Management
Oversight; Audit; Compensation; Nominating and Corporate Governance; and
Health, Safety and Environment. Each Committee's charter is to be reviewed
periodically by the Committee and the Board.
 
  2. Composition of Committees. It is the policy of the Board that only non-
employee Directors serve on Board Committees.
 
  A Director who is part of an interlocking directorate (i.e. one in which the
Chief Executive Officer or another executive officer of the Company serves on
the board of another corporation that employs the Director) may not serve on
the Compensation Committee. The composition of the Compensation Committee will
be reviewed annually to ensure that each of its members meet the criteria set
forth in applicable SEC and IRS rules and regulations.
 
                                      10
<PAGE>
 
  3. Assignment and Rotation of Committee Members. The Nominating and
Corporate Governance Committee, with direct input from the Chief Executive
Officer, recommends to the Board the membership of the various Committees and
their Chairmen and the Board approves the Committee assignments. In making its
recommendations to the Board, such Committee takes into consideration the need
for continuity, subject matter expertise, tenure and the desires of individual
Board members.
 
  4. Frequency and Length of Committee Meetings. The Board and Committee
meeting schedule for each year is submitted and approved by the Board in
advance. The number of regularly scheduled meetings per year are as follows:
Management Oversight--5; Audit--3; Compensation--3; Nominating and Corporate
Governance--2; and Health, Safety and Environment--2. In addition, the
Chairman of a Committee may call a special meeting at any time if deemed
advisable. Accommodations will be made on a case by case basis should a
Committee agenda require more time than initially scheduled.
 
  5. Committee Agendas; Reports to the Board. Appropriate members of
management and staff will prepare draft agenda and related background
information for each Committee meeting which, to the extent desired by the
relevant Committee Chairman, will be reviewed and approved by such Chairman in
advance of distribution to the other members of the Committee. A forward
agenda of recurring topics to be discussed during the year will be prepared
for each Committee and furnished to all Directors. Each Committee member is
free to suggest items for inclusion on the agenda and to raise at any
Committee meeting subjects that are not on the agenda for that meeting.
 
  Reports on each Committee meeting (other than Management Oversight Committee
meetings) are made to the full Board. All Directors are furnished copies of
each Committee's minutes.
 
Other Board Practices
 
  1. Director Orientation. It is the sense of the Board that an orientation
program be developed for new Directors which will include comprehensive
information about the Company's business and operations; general information
about the Board and its Committees, including a summary of Director
compensation and benefits; and a review of Director duties and
responsibilities. Some of such topics will be included in a Director's
handbook and others will be covered in meetings with key executives.
 
  2. Board Interaction With Institutional Investors and Other
Stakeholders. The Board believes that it is senior management's responsibility
to speak for the Company. Individual Board members may, from time to time,
meet or otherwise communicate with outside constituencies that are involved
with the Company. In those instances, however, it is expected that Directors
will do so only with the knowledge of senior management and, absent unusual
circumstances, only at the request of senior management.
 
  3. Periodic Review of These Guidelines. The operation of the Board of
Directors is a dynamic and evolving process. As such these Guidelines will be
reviewed periodically by the Nominating and Corporate Governance Committee and
any recommended revisions will be submitted to the full Board for action
thereon.
 
                                      11
<PAGE>
 
          THE BOARD OF DIRECTORS AND STANDING COMMITTEES OF DIRECTORS
 
  The Board of Directors of the Company has standing Audit; Compensation;
Nominating and Corporate Governance; Health, Safety and Environment; and
Management Oversight Committees. Each of the standing Committees is comprised
entirely of outside Directors, none of whom is an employee or former employee
of the Company. During the last fiscal year, the Board of Directors met on 9
occasions, the Audit Committee met on 3 occasions, the Compensation Committee
met on 4 occasions, the Nominating and Corporate Governance Committee met on 2
occasions, the Health, Safety and Environment Committee met on 2 occasions,
and the Management Oversight Committee met on 5 occasions. Except for Lawrence
S. Eagleburger, no member of the Board attended fewer than 75 percent of the
aggregate number of meetings of the Board and the Committees on which he or
she served during the last fiscal year.
 
Audit Committee
 
  The Audit Committee has, among other things, responsibility for recommending
the appointment of independent auditors to the Board of Directors; reviewing
the scope of the independent auditors' examination and the scope of activities
of the internal audit department; reviewing the Company's financial policies
and accounting systems and controls; and approving and ratifying the duties
and compensation of the independent auditors, both with respect to audit and
non-audit services. The Committee also reviews the Company's compliance with
its Code of Business Conduct. The Committee meets separately from time to time
with the independent auditors and with members of the internal audit staff,
outside the presence of Company management or other employees, to discuss
matters of concern, to receive recommendations or suggestions for change and
to exchange relevant views and information.
 
Compensation Committee
 
  Duties of the Compensation Committee include developing and approving an
overall executive compensation philosophy consistent with corporate objectives
and stockholder interests; acting as a salary and promotion committee with
respect to certain officers of the Company and its subsidiaries and
affiliates; establishing annual performance criteria and reward schedules
under the Company's Annual Performance Pay Plan and certifying the performance
level achieved and reward payments at the end of each plan year; approving any
other incentive or bonus plans applicable to certain officers of the Company's
subsidiaries and affiliates; administering awards under the Company's 1993
Stock and Long-Term Incentive Plan and Senior Executives' Deferred
Compensation Plan; approving agreements or arrangements relating to the terms
of employment, continued employment or termination of employment for certain
officers of the Company and its subsidiaries and affiliates; acting as a
committee for administration of other forms of non-salary compensation; and
reviewing periodically the Company's Director compensation practices and
recommending to the Board any changes thereto.
 
Nominating and Corporate Governance Committee
 
  The Nominating and Corporate Governance Committee periodically reviews and
updates the criteria for Board membership and evaluates the qualifications of
each Director candidate against such criteria; assesses the appropriate mix of
skills and characteristics required of Board members; identifies and screens
candidates for Board membership; establishes procedures whereby individuals
may be recommended by stockholders for consideration by the Committee as
possible candidates for election to the Board; reviews annually each
Director's continuation on the Board and recommends to the Board a slate of
Director nominees for election at the Annual Meeting of Stockholders;
recommends candidates to fill vacancies on the Board; reviews periodically the
status of each Director to assure compliance with the Board's policy that at
least a majority of Directors meet the Board's definition of "independent
Director"; recommends members to serve on the standing
 
                                      12
<PAGE>
 
Committees of the Board and the Chairmen thereof; and reviews periodically the
corporate governance guidelines adopted by the Board of Directors and
recommends revisions thereto as deemed appropriate.
 
  The Nominating and Corporate Governance Committee will consider qualified
nominees recommended by stockholders who may submit recommendations to the
Committee in care of the Vice President and Secretary at the address of the
Company set forth on page 1 of this Proxy Statement. Stockholder nominations
must be submitted prior to year end and must be accompanied by a description
of the qualifications of the proposed candidate and a written statement from
the proposed candidate that he or she is willing to be nominated and desirous
of serving, if elected.
 
  Nominations by stockholders may also be made at an Annual Meeting of
Stockholders in the manner provided in the Company's By-laws. The By-laws
provide that a stockholder of the Company entitled to vote for the election of
Directors may make nominations of persons for election to the Board at a
meeting of stockholders by complying with required notice procedures. Such
nominations shall be made pursuant to written notice to the Secretary, which
must be received at the principal executive offices of the Company not less
than ninety (90) days prior to the anniversary date of the immediately
preceding Annual Meeting of Stockholders. The notice shall set forth (a) as to
each person the stockholder proposes to nominate for election or re-election
as a Director, (i) the name, age, business address and residence address of
the person, (ii) the principal occupation or employment of the person, (iii)
the class and number of shares of capital stock of the Company that are
beneficially owned by the person, and (iv) all other information relating to
the person that is required to be disclosed in solicitations for proxies for
election of directors pursuant to Regulation 14A under the Securities Exchange
Act of 1934, as amended; and (b) as to the stockholder giving the notice, (i)
the name and record address of the stockholder, and (ii) the class and number
of shares of capital stock of the Company that are beneficially owned by the
stockholder. The Company may require any proposed nominee to furnish such
other information as may reasonably be required by the Company to determine
the eligibility of such proposed nominee to serve as a Director of the
Company. At any meeting of stockholders, the presiding officer may disregard
the purported nomination of any person not made in compliance with the above-
specified procedures.
 
Health, Safety and Environment Committee
 
  The Health, Safety and Environment Committee has responsibility for
reviewing and assessing the Company's health, safety and environmental
policies and practices and proposing modifications or additions thereto as
needed; overseeing the communication and implementation of such policies
throughout the Company; reviewing annually the health, safety and
environmental performance of the Company's operating units and their
compliance with applicable policies and legal requirements; and identifying,
analyzing and advising the Board on health, safety and environmental trends
and related emerging issues.
 
Management Oversight Committee
 
  The Management Oversight Committee has responsibility for evaluating the
performance of the Chief Executive Officer of the Company; reviewing
succession plans for senior management of the Company and its major operating
units; evaluating management development programs and activities; and
reviewing other internal matters of broad corporate significance.
 
          COMPENSATION COMMITTEE INTERLOCKS AND INSIDER PARTICIPATION
 
  The following persons served as members of the Compensation Committee during
1998: Robert L. Crandall, W. R. Howell, Delano E. Lewis, C. J. Silas and Ray
L. Hunt (September 29-December 31, 1998), none of whom is an officer or former
officer of the Company or its subsidiaries or had a relationship with the
Company or its subsidiaries requiring director interlock or insider
participation disclosure.
 
                                      13
<PAGE>
 
            COMPENSATION COMMITTEE REPORT ON EXECUTIVE COMPENSATION
 
  The Company's primary mission is to enhance long-term shareholder value by
providing a broad spectrum of high quality services and related products
within the energy services, engineering and construction and equipment
manufacturing business segments in which the Company operates. The
Compensation Committee of Directors (the "Committee") believes that the
Company's total compensation package for executives should be linked
principally to increased shareholder value and to measures which drive
shareholder value.
 
  The Committee has responsibility for overseeing the compensation program for
the members of the Executive Committee of the Company (composed at the end of
1998 of the four most senior executive officers) and other senior officers of
the Company and its business units.
 
Overall Executive Compensation Philosophy
 
  The overriding objective of the total compensation package for senior
executives is to emphasize the enhancement of shareholder value. Beyond this,
the Committee's priorities are to establish and maintain competitive executive
compensation programs that enable the Company to attract, retain, and motivate
the high caliber executives required for the success of the business. In
determining what it deems to be appropriate types and amounts of compensation
for executive officers, the Committee consults with outside compensation
consultants and reviews independent compensation data.
 
  In the design and administration of executive compensation programs, the
Committee refers to, but does not necessarily target, current market levels at
the 50th percentile. In doing so, the Committee considers the competitive
market data for two comparator groups: (i) specific peer companies within the
energy services, engineering and construction and equipment manufacturing
industries, and (ii) similarly sized companies within general industry which,
in the Committee's opinion, provide the most comparable references for the
Company's senior executive positions. Regression analysis is used in assessing
all market data to mitigate the impact of company size on compensation levels.
 
  The Committee considers total compensation, as well as each component of the
compensation package, in determining actual compensation levels. The total
compensation package is expected in most instances to result in payments at
market levels, given acceptable corporate and/or business unit performance,
and above market levels, given outstanding performance.
 
  The Committee believes its objectives can be optimized by providing
executives with a compensation package that consists of a cash base salary, a
rewards-oriented compensation program aligned with shareholder value creation,
stock-based awards and supplemental retirement benefits.
 
Compensation Considerations Related to the Dresser Merger
 
  Anticipating the increase in scope and responsibilities for executives who
would become the management team for the Company after the merger with
Dresser, the Committee sought outside compensation expertise to advise it on
appropriate compensation packages for the new organization. The Committee
considered the consultant's recommendations and concluded that the Company's
current executive compensation philosophy, which resulted in the design of the
existing executive compensation programs, would remain viable and competitive
for the new organization, but that the comparable references for competitive
market data would need to be changed to reflect a much larger company
following the merger. For senior executive officers, a new set of general
industry companies were selected as comparable on the basis of their size and
their superior performance as measured by 5-year total shareholder return and
1- and 5-year return on capital. Senior officer positions within the Company's
business units were compared to specific peer companies in the energy
services, engineering and construction and equipment manufacturing industries.
 
                                      14
<PAGE>
 
Compensation Arrangement For Chief Executive Officer
 
  In 1995, the Company entered into an agreement with Mr. Cheney covering the
terms of his employment by the Company. Mr. Cheney's employment agreement,
which was approved by the Board of Directors and the Committee, provides for a
total compensation package which reflects the Company's objectives of aligning
significant compensation opportunity with the interests of stockholders and
building executive stock ownership. Mr. Cheney's employment agreement with the
Company is summarized beginning on page 23 of this Proxy Statement.
 
Base Salary
 
  Ordinarily, base salaries for the executive officers, including Mr. Cheney,
are reviewed each December by the Committee. In 1998, executive officer base
salaries were reviewed mid-year in anticipation of the Dresser Merger.
Adjustments to base salaries for executive officers were made effective
October 1, 1998, following the completion of the merger. In addition to
considering market comparisons in making salary decisions, the Committee
exercised discretion and judgment based on the following factors: the
executive's level of responsibility in the new organization, experience in
his/her role, and equity issues relating to pay for other Company executives,
as well as external factors involving competitive positioning, projected
overall corporate performance, and general economic conditions. No specific
formula is applied to determine the weight of each factor.
 
  Mr. Cheney's base salary for 1998 was increased to $1.150 million beginning
January 1, 1998. On October 1, 1998 Mr. Cheney's annual base salary was
increased to $1.283 million to reflect expanded duties and responsibilities of
the new organization. In determining Mr. Cheney's base salary, the Committee
considered each of the above factors, although primary consideration was given
to his individual contributions to the Company. The Committee's action
increasing Mr. Cheney's base salary acknowledges his strong leadership in
guiding the Company through a successful merger, positioning the Company for
long term financial stability, and the successful undertaking of various
initiatives to achieve the synergies of the combined organization and to
better align the business units and reduce overhead costs.
 
Annual Performance Pay Plan
 
  As a means of strengthening the link between total cash compensation and the
Company's performance, effective January 1, 1995, the Committee adopted an
intermediate term reward-oriented program (the "Annual Performance Pay Plan")
based on cash value added ("CVA"). CVA measures the difference between after
tax cash income and a capital charge based upon the Company's weighted average
cost of capital to determine the amount of value, in terms of cash flow, added
to the business. CVA has been demonstrated to provide a close correlation to
total shareholder return; therefore, incentive awards are closely linked to
the improvement of shareholder value.
 
  At the beginning of each plan year, the Committee establishes a reward
schedule which aligns given levels of CVA performance beyond a threshold level
with reward opportunities, such that the level of achievement of annual CVA
performance will determine the amount of incentive compensation payable to a
participant. In order to maximize the link between the compensation earned
under the Annual Performance Pay Plan and shareholder value creation and to
focus executives' attention on a time frame longer than one year, only one-
half of the bonus earned in the current year is paid in cash. The remaining
one-half of the bonus is converted into Company Common Stock equivalents and
paid in cash in annual installments in each of the next two years, each
installment based on the then value of one-half the stock equivalents.
 
  Officers of the Company and its business units and certain senior managers
were eligible to participate in the Annual Performance Pay Plan during 1998.
In 1998, consolidated CVA performance did not meet the target level
established by the Committee and, accordingly, Messrs. Cheney, Coleman, Jones,
Lesar, and LeSuer earned no incentive award under the provisions of the Annual
Performance Pay Plan. Messrs. Bradford and Vaughn did
 
                                      15
<PAGE>
 
not participate in the Annual Performance Pay Plan during 1998, but rather in
Dresser's annual incentive plan, which plan's 1998 performance goals were
approved by Dresser's board prior to the Dresser Merger. The bonuses earned by
Messrs. Bradford and Vaughn under the Dresser annual incentive plan are shown
in the Summary Compensation Table.
 
  Special Bonus. In December 1998, the Committee authorized a special, one-
time cash bonus to be paid to selected officers (including three of the
executive officers listed in the Summary Compensation Table) and key employees
whose hard work had been instrumental in bringing the Dresser Merger to its
successful completion and whose future contributions will be required to
realize the synergies of the combination. The special bonus amounts received
by Messrs. Cheney, Lesar and Coleman are set forth in the Summary Compensation
Table.
 
Stock-Based Compensation
 
  The 1993 Plan provides for a variety of cash and stock-based awards
(including stock options, stock appreciation rights, and restricted stock,
among others) which the Committee may, in its discretion, select in
establishing individual long-term incentive awards or use as it deems
appropriate in specific recruiting and hiring situations.
 
  Stock options were an important long-term incentive granted to executive
officers in 1998. Stock options granted in 1998 are exercisable at the fair
market value of the Company Common Stock on the date of grant and become
exercisable during employment over a three-year period (one-third per year).
Options, which have value only if the stock price appreciates following the
date of grant, provide an excellent means for linking executives' interests
directly to those of stockholders. Although a great number of executives'
roles had been expanded at the advent of the merger with Dresser, the number
of option shares awarded to individual executives in the December review was
generally consistent with past practice.
 
  The Committee's determination of the number of option shares granted to
executive officers, including the grants made to Mr. Cheney, was based on a
subjective assessment of organizational roles and internal job relationships,
and on references to competitive practices in long-term incentive
opportunities for comparable positions within similarly sized, high-performing
companies in general industry. An option for 100,000 shares was granted to Mr.
Cheney in December 1998.
 
  In furtherance of the Committee's philosophy to tie shareholder value
enhancement to compensation opportunities, it is a stated objective of the
Committee to broaden the base of employee stock ownership throughout the
Company. Accordingly, in December 1998, stock option grants of an aggregate
3,417,000 shares were made to approximately 3,000 managerial employees. The
Committee's intention is to continue this process with additional grants in
the future in order to drive stock option grants deeper into the organization.
 
  The Committee made use of restricted stock grants at the close of the merger
in the fall of 1998 in order to tie executive management of the new
organization closely to future Company financial performance. Seventeen
officers received restricted stock grants totaling 367,500 shares. These
awards recognized their expanded responsibilities and current and future
contributions, as well as served to build their stock ownership in the
Company. A restricted stock award of 50,000 shares was granted to Mr. Cheney
in October 1998.
 
Senior Executives' Deferred Compensation Plan
 
  Under the terms of the Senior Executives' Deferred Compensation Plan (the
"SEDC Plan"), which is used for the purpose of providing supplemental
retirement benefits to senior executives, (i) mandatory additions to a
participant's account are made to offset contributions to which each would
have been entitled under the Company's qualified defined contribution plans if
not for the limitation on contributions imposed under the Internal Revenue
Code (commonly known as ERISA Offset Benefits), (ii) additions up to the
amount of any remuneration which would otherwise exceed the deduction limit
under Section 162(m) of the Internal Revenue Code may be allocated to a
participant's account in lieu of the payment of such remuneration, and (iii)
 
                                      16
<PAGE>
 
discretionary additions, in such amounts as the Committee may determine, are
made to provide additional supplemental retirement benefits ("Supplemental
Retirement Benefit"). Interest on active and retired participants'
Supplemental Retirement Benefit accounts is accrued at the rate of five and
ten percent per annum, respectively, while interest on the other two account
balances accrues at the rate of ten percent per annum. No amounts may be
received by a participant under the SEDC Plan prior to termination of such
participant's employment.
 
  In making Supplemental Retirement Benefit contributions under the SEDC Plan,
amounts are determined considering guidelines that include references to
retirement benefits provided from other programs, compensation, length of
service with the Company and as an officer, and years of service to normal
retirement. There is no specific weighting of these factors. The Committee
authorized a 1998 Supplemental Retirement Benefit addition for Mr. Cheney of
$500,000, the minimum amount specified in his employment agreement.
 
Policy Regarding Section 162(m) of the Internal Revenue Code
 
  Section 162(m) of the Internal Revenue Code and the regulations promulgated
thereunder generally disallow a federal income tax deduction by a public
company for compensation paid to the chief executive officer or any of the
four other most highly compensated officers to the extent such compensation
exceeds $1 million in any year, excluding certain performance-based
compensation and compensation which is deferred.
 
  The Company's policy is to utilize available tax deductions whenever
appropriate, and the Committee, when determining executive compensation
programs, considers all relevant factors, including the tax deductions that
may result from such compensation. Accordingly, the Company has attempted to
preserve the federal tax deductibility of compensation in excess of $1 million
a year to the extent such is consistent with the intended objectives of the
Committee's executive compensation philosophy.
 
  The 1993 Stock and Long-Term Incentive Plan (the "1993 Plan") was amended by
the stockholders in 1996 to qualify stock options and stock appreciation
rights granted thereunder as performance-based compensation under IRS rules.
The Committee decided, however, not to make the necessary changes to qualify
the Annual Performance Pay Plan (which was discussed above) for tax
deductibility under Section 162(m) since to do so would have limited the
Committee's flexibility in the administration of the Plan. The Committee
believes that the best interests of the Company and its stockholders are
served by its current executive compensation programs, which encourage and
promote the Company's principal compensation objective, enhancement of
shareholder value, and permit the Committee to exercise discretion in the
design and implementation of compensation packages. Accordingly, the Company
may from time to time pay compensation to its executive officers that may not
be fully deductible. Because of the mandatory deferral provisions relating to
payment of incentive compensation earned under the Annual Performance Pay Plan
and the elective deferral by certain executive officers of portions of their
salary and incentive compensation, the loss of deductibility for 1998 is not
expected to be significant. The Committee will continue to review the
Company's executive compensation plans periodically to determine what changes,
if any, should be made as the result of the limitation on deductibility.
 
                                          Respectfully submitted,
 
                                          THE COMPENSATION COMMITTEE OF
                                           DIRECTORS
 
                                          Robert L. Crandall
                                          W. R. Howell
                                          Ray L. Hunt*
                                          Delano E. Lewis
                                          C. J. Silas
 
- --------
* During 1998, Mr. Hunt served on the Committee from September 29, 1998
through December 31, 1998.
 
                                      17
<PAGE>
 
                COMPARISON OF FIVE-YEAR CUMULATIVE TOTAL RETURN
 
  The following graph compares the Company's cumulative total stockholder
return on its Common Stock for the five-year period ended December 31, 1998,
with the Standard & Poor's 500 Stock Index ("S&P 500") and the Standard &
Poor's Energy Composite Index ("S&P Energy Composite") over the same period.
This comparison assumes the investment of $100 on December 31, 1993 and the
reinvestment of all dividends. On January 23, 1996, the Company distributed to
stockholders all of the outstanding common stock of Highlands Insurance Group,
Inc. as a special dividend. The graph accounts for this distribution as though
it were paid in cash and reinvested in Company Common Stock. The stockholder
return set forth on the chart below is not necessarily indicative of future
performance.
 
                    Total Stockholders' Return--Five Years
 Assumes Investment of $100 on December 31, 1993 and Reinvestment of Dividends
 
                       [PERFORMANCE GRAPH APPEARS HERE]
 
 
<TABLE>
<CAPTION>
                                        12-31-  12-31-  12-31-  12-31-
                               12-31-93   94      95      96      97    12-31-98
                               -------- ------- ------- ------- ------- --------
  <S>                          <C>      <C>     <C>     <C>     <C>     <C>
  Halliburton Company.........   $100   $107.27 $168.11 $212.64 $370.62 $214.62
  S&P 500.....................   $100   $101.32 $139.40 $171.40 $228.58 $293.91
  S&P Energy Composite........   $100   $103.84 $135.78 $170.78 $213.90 $215.05
</TABLE>
 
                                      18
<PAGE>
 
                          SUMMARY COMPENSATION TABLE
 
<TABLE>
<CAPTION>
                                      Annual Compensation             Long-Term Compensation
                               ---------------------------------- ------------------------------
                                                                         Awards         Payouts
                                                                  --------------------- --------
                                                                  Restricted Securities
                                                     Other Annual   Stock    Underlying   LTIP    All Other
   Name and Principal                       Bonus    Compensation   Awards    Options   Payouts  Compensation
        Position          Year Salary ($)   ($)(1)      ($)(2)      ($)(3)     (#)(4)    ($)(5)     ($)(6)
   ------------------     ---- ---------- ---------- ------------ ---------- ---------- -------- ------------
<S>                       <C>  <C>        <C>        <C>          <C>        <C>        <C>      <C>
William E. Bradford(7)..  1998 $1,001,000 $1,672,708      --      $1,886,086   72,804   $462,194   $436,057
 Chairman of the Board
  of                      1997        N/A        N/A     N/A             N/A      N/A        N/A        N/A
 the Company              1996        N/A        N/A     N/A             N/A      N/A        N/A        N/A
Richard B. Cheney.......  1998  1,183,257  1,154,704      --       1,525,000  100,000        N/A    564,771
 Chief Executive Officer
  of                      1997  1,100,000  1,980,000      --               0  100,000        N/A    617,943
 the Company              1996  1,000,000  1,125,000      --               0  360,000        N/A    582,147
Lester L. Coleman.......  1998    412,506    225,000      --         469,375   25,000        N/A    173,581
 Executive Vice
  President               1997    390,000    390,000      --               0   20,000        N/A    127,193
 and General Counsel of   1996    390,000    202,500      --               0   74,000        N/A    130,232
 the Company
Dale P. Jones(7)........  1998    500,000          0      --               0        0        N/A    546,644
 Vice Chairman of the     1997    500,000    650,000      --               0   50,000        N/A     91,759
 Company                  1996    500,000    540,000      --               0  180,000        N/A    115,919
David J. Lesar..........  1998    693,255    534,955      --       1,525,000   65,000        N/A    308,524
 President and Chief      1997    500,000    650,000      --       3,868,750   60,000        N/A    187,553
 Operating Officer of
  the                     1996    391,875    540,000      --       1,120,000  110,000        N/A    134,866
 Company
Ken R. LeSuer(7)........  1998    500,000          0      --               0        0        N/A    696,333
 Vice Chairman of the     1997    475,000    617,500      --               0   50,000        N/A    302,604
 Company                  1996    425,000    540,000      --         591,250  160,000        N/A    190,233
Donald C. Vaughn(7).....  1998    614,417  1,085,000      --       1,668,155   18,037        N/A    173,569
 Vice Chairman of the     1997        N/A        N/A     N/A             N/A      N/A        N/A        N/A
 Company                  1996        N/A        N/A     N/A             N/A      N/A        N/A        N/A
</TABLE>
- --------
(1) The Compensation Committee approved a special one-time bonus for selected
    officers and key employees, including Messrs. Cheney, Coleman and Lesar.
    Messrs. Bradford and Vaughn received the bonuses earned under the Dresser
    incentive compensation plan which were approved prior to the Dresser
    Merger.
(2) The dollar value of perquisites and other personal benefits for each of
    the named executive officers was less than established reporting
    thresholds.
(3) In 1996, Mr. Lesar had two awards of 20,000 shares each on which
    restrictions will lapse over a 10-year period and Mr. LeSuer was awarded
    20,000 shares with restrictions lapsing over a 5-year period. In 1997, Mr.
    Lesar was awarded 100,000 shares with restrictions lapsing over a 10-year
    period. In 1998, Messrs. Bradford, Cheney and Vaughn were each awarded
    50,000 shares with restrictions lapsing over 5 years; Mr. Lesar was
    granted 50,000 shares lapsing over 10 years; and Mr. Coleman was granted
    15,000 shares lapsing over 10 years. In addition, during 1998, Messrs.
    Bradford and Vaughn were issued 8,861 and 3,513 restricted shares,
    respectively, pursuant to restricted incentive stock awards granted under
    Dresser's stock compensation plan. Restrictions on such shares lapsed on
    the Effective Date of the Dresser Merger. The total number and value of
    restricted shares held by each of the above individuals as of December 31,
    1998 were as follows:
 
<TABLE>
<CAPTION>
                                                             Total    Aggregate
                                                           Restricted   Market
      Name                                                   Shares     Value
      ----                                                 ---------- ----------
      <S>                                                  <C>        <C>
      Mr. Bradford........................................   50,000   $1,481,250
      Mr. Cheney..........................................  175,000    5,184,375
      Mr. Coleman.........................................   32,000      948,000
      Mr. Jones*..........................................        0            0
      Mr. Lesar...........................................  186,000    5,510,250
      Mr. LeSuer..........................................   19,900      589,538
      Mr. Vaughn..........................................   50,000    1,481,250
</TABLE>
 
  * Restrictions lapsed on 29,800 shares with a market value of $826,245 due
    to retirement on October 2, 1998.
  Dividends are paid on the restricted shares.
 
                                      19
<PAGE>
 
(4) Solely as a result of a one-time change in the timing of option grants to
    senior executives, the named persons (other than Messrs. Bradford and
    Vaughn) received two grants in 1996.
(5) The Company does not have a long-term incentive program. Mr. Bradford
    received long-term incentive payouts in January 1998 and 1999 under
    Dresser's performance stock unit program.
(6) "All Other Compensation" includes the following accruals for or
    contributions to various plans for the fiscal year ending December 31,
    1998: (i) Company contributions to qualified defined contribution
    retirement plans for Mr. Bradford -- $1,156, Mr. Cheney -- $6,400, Mr.
    Coleman -- $6,400, Mr. Jones -- $6,400, Mr. Lesar -- $6,400, Mr. LeSuer --
    $6,400 and Mr. Vaughn -- $4,800; (ii) 401(k) plan matching contributions for
    Mr. Bradford -- $3,083, Mr. Cheney -- $3,200, Mr. Coleman -- $3,200, Mr.
    Jones -- $3,200, Mr. Lesar --$3,200, Mr. LeSuer -- $3,200 and Mr. Vaughn --
    $6,400; (iii) ERISA limitation accruals for Mr. Bradford --$387,447, Mr.
    Cheney --$40,930, Mr. Coleman -- $10,100, Mr. Jones --$10,290, Mr. Lesar --
    $21,330, Mr. LeSuer -- $13,600 and Mr. Vaughn --$96,964; (iv) supplemental
    retirement plan contributions for Mr. Cheney -- $500,000, Mr. Coleman --
    $133,000, Mr. Jones -- $500,000, Mr. Lesar -- $250,000 and Mr. LeSuer --
    $625,000; (v) above-market earnings on ERISA limitation account for Mr.
    Cheney -- $6,314, Mr. Coleman -- $3,984, Mr. Jones -- $6,500, Mr. Lesar --
    $2,638 and Mr. LeSuer -- $3,814; (vi) above-market earnings on amounts
    deferred under elective deferral plans for Mr. Bradford -- $23,650, Mr.
    Cheney -- $7,927, Mr. Coleman -- $16,897, Mr. Jones --$20,255, Mr. Lesar --
    $24,955, Mr. LeSuer -- $44,319 and Mr. Vaughn -- $13,960; and (vii) Company
    contributions to executive life insurance premiums for Mr. Bradford --
    $20,721 and Mr. Vaughn -- $5,410. Mr. Vaughn was credited with earnings of
    $46,035 on his accrued balance under an unfunded plan provided by a
    subsidiary in lieu of normal pension benefits.
(7) Messrs. Bradford and Vaughn became executive officers of the Company on
    September 29, 1998. Messrs. Jones and LeSuer ceased to be executive
    officers on September 29, 1998.
 
                       OPTION GRANTS IN LAST FISCAL YEAR
 
<TABLE>
<CAPTION>
                                      % of
                                      Total
                         Number of   Options                           Potential Realizable Value
                         Securities  Granted                           at Assumed Annual Rates of
                         Underlying    to                             Stock Price Appreciation for
  Individual Grants(1)    Options   Employees Exercise                       Option Term(2)
  --------------------    Granted   in Fiscal   Price      Expiration -------------------------------
          Name              (#)       Year    ($/Share)       Date         5%               10%
          ----           ---------- --------- ---------    ---------- -------------    --------------
<S>                      <C>        <C>       <C>          <C>        <C>              <C>
William E. Bradford.....    24,268      .70   $36.8125      01/15/08  $     561,833    $    1,423,795
                            24,268      .70    38.8125      01/15/08        592,357         1,501,149
                            24,268      .70    40.8125      01/15/08        622,881         1,578,503
Richard B. Cheney.......   100,000     2.88    28.1250      12/02/08      1,768,766         4,482,401
Lester L. Coleman.......    25,000      .72    28.1250      12/02/08        442,192         1,120,600
Dale P. Jones...........       N/A
David J. Lesar..........    65,000     1.87    28.1250      12/02/08      1,149,698         2,913,560
Ken R. LeSuer...........       N/A
Donald C. Vaughn........     6,013      .17    36.8125      01/15/08        139,208           352,781
                             6,012      .17    38.8125      01/15/08        146,747           371,885
                             6,012      .17    40.8125      01/15/08        154,309           391,048
All Optionees........... 3,466,848   100.00    31.7079(3)     (3)        69,132,166       175,194,482
All Stockholders........       N/A      N/A        N/A        N/A     8,772,997,785(4) 22,232,498,860(4)
</TABLE>
- --------
(1) All options granted under the 1993 Plan are granted at the fair market
    value of the Common Stock on the grant date and generally expire ten years
    from the grant date. During employment options vest over a three year
    period, with one-third of the shares becoming exercisable on each of the
    first, second and third anniversaries of the grant date.
    Options for Messrs. Bradford and Vaughn were granted under the Dresser stock
    compensation plan and are shown at the exercise price and in the sequence
    they first become exercisable, respectively: July 15, 1998, January 15, 1999
    and January 15, 2000. Messrs. Bradford's and Vaughn's option grants were
    made in three approximately equal installments. The exercise price of the
    first installment of each grant was the average high and low trading prices
    of Dresser's common stock on the date of grant and the exercise prices of
    the second and third installments are, respectively, $2 and $4 higher than
    that of the first installment. Such options were coupled with a total of
    14,559 and 3,606 restricted incentive stock ("RIS") awards to Messrs.
    Bradford and Vaughn, respectively. Pursuant to the Dresser stock
    compensation plan, recipients of RIS awards will be issued, upon exercise of
    the related option while actively employed by the Company, one share of
    restricted stock for every five option shares exercised. Provided the
    related option shares are held on that date, restrictions on the restricted
    shares lapse on the third anniversary of the date of issue or, if earlier,
    upon termination of employment by reason of death, disability or approved
    retirement. If the related option shares are sold or otherwise transferred
    prior to lapse of restrictions, the restricted shares are forfeited.
(2) The assumed values result from certain prescribed rates of stock price
    appreciation. Values were calculated based on a 10-year exercise period
    for all grants. The actual value of the option grants is dependent on
    future performance of the Common Stock and overall stock market
    conditions. There is no assurance that the values reflected in this table
    will be achieved. The Company did not use an alternative formula for a
    grant date valuation, as it is not aware of any formula that will
    determine with reasonable accuracy a present value based on future unknown
    or volatile factors.
(3) The exercise price shown is a weighted average of all options granted in
    1998. Options expire on one or more of the following dates: January 15,
    2008, February 2, 2008, March 19, 2008, June 2, 2008, June 4, 2008, June
    8, 2008, August 7, 2008, September 14, 2008, October 8, 2008 or December
    2, 2008.
(4) "All Stockholders" values are calculated using the weighted average
    exercise price for all options awarded in 1998, $31.7079, based on the
    outstanding shares of Common Stock on December 31, 1998.
 
                                      20
<PAGE>
 
                AGGREGATED OPTION EXERCISES IN LAST FISCAL YEAR
                       AND FISCAL YEAR-END OPTION VALUES
 
<TABLE>
<CAPTION>
                                                  Number of Securities
                                                 Underlying Unexercised     Value of Unexercised
                           Shares                Options at Fiscal Year-   In-the-Money Options at
                          Acquired     Value          End (Shares)           Fiscal Year-End ($)
                         on Exercise  Realized  ------------------------- -------------------------
          Name               (#)        ($)     Exercisable Unexercisable Exercisable Unexercisable
          ----           ----------- ---------- ----------- ------------- ----------- -------------
<S>                      <C>         <C>        <C>         <C>           <C>         <C>
William E. Bradford.....   72,804    $1,430,438   189,714      391,561    $  689,023    $      0
Richard B. Cheney.......        0             0   673,334      286,666     3,823,334     324,166
Lester L. Coleman.......        0             0   128,001       62,999       872,793      74,457
Dale P. Jones...........        0             0   293,335       93,333     1,876,473      87,084
David J. Lesar..........        0             0   175,336      141,666       835,860     131,042
Ken R. LeSuer...........        0             0   276,335       86,665     2,024,648      86,664
Donald C. Vaughn........   18,037       342,534    87,683      189,124       590,595           0
</TABLE>
 
                                       21
<PAGE>
 
                               RETIREMENT PLANS
 
  Executives of Halliburton Company are participating or have participated in
several defined benefit pension plans of the Company. Messrs. Cheney, Coleman,
Jones, Lesar and LeSuer were covered by the Halliburton Retirement Plan (the
"Floor Plan"). Messrs. Bradford and Vaughn are covered by the Dresser
Supplemental Executive Retirement Plan which is a non-qualified plan and by
certain frozen defined benefit plans that were sponsored by Dresser or its
subsidiaries.
 
  The purpose of the Halliburton Floor Plan was to provide a floor for
retirement benefits provided under the Halliburton Profit Sharing and Savings
Plan (the "Halliburton Profit Sharing Plan"). Effective as of December 31,
1996, benefit accruals under the Floor Plan ceased for all employees except
those age 55 or over ("Grandfathered Employees"). The portion of the Floor
Plan attributable to employees other than Grandfathered Employees terminated
effective February 28, 1997 and all accrued benefits payable to participants
were distributed in 1998.
 
  The Halliburton Profit Sharing Plan is intended to be the primary plan to
provide retirement benefits to participating employees. The Company makes
annual contributions from profits to the Halliburton Profit Sharing Plan. Such
contributions may not be less than 10% of profits, as defined in the Plan
(reduced by certain retirement plan expenses), except that such contributions
may not exceed the maximum amount deductible under Section 404 of the Internal
Revenue Code and may not be less than 4% of participating employees'
compensation. It is not possible to estimate the amount of benefits payable at
retirement under the Halliburton Profit Sharing Plan to Messrs. Cheney,
Coleman and Lesar because of some or all of the following: (i) amounts
contributed in the future will be contingent on future profits, (ii) earnings
on trust fund assets will vary, (iii) trust fund assets may appreciate or
depreciate in value, (iv) the compensation of the individual may vary, (v) age
at date of retirement may vary, and (vi) the Plan may be changed or
discontinued. Messrs. Jones and LeSuer retired from the Company in October
1998 and January 1999, respectively. Messrs. Bradford and Vaughn did not
participate in the Halliburton Profit Sharing Plan during 1998.
 
  The Floor Plan is a qualified defined benefit pension plan established as of
January 1, 1991 as a floor plan integrated with the Halliburton Profit Sharing
Plan to provide an adequate level of retirement benefits for employees. Prior
to January 1, 1997, the terms of the Floor Plan provided for a monthly pension
payment equal to the following amount: (i) 1 1/3% of an employee's average
monthly base compensation (computed over the highest three calendar year
period) multiplied by such employee's years of accrual service after January
1, 1990; minus (ii) a pension which is the actuarial equivalent of the
participant's eligible profit sharing accounts (excluding any employer and
employee contributions under the employee savings portion of the program)
accumulated since January 1, 1990 under the Halliburton Profit Sharing Plan.
The offset for the Halliburton Profit Sharing Plan was based upon the 1984
Unisex Pension Mortality Table and an 8 1/2% interest assumption. As a result
of the termination of the Floor Plan as to employees other than Grandfathered
Employees, such employees received a distribution of such Floor Plan benefit,
if any, in 1998. The Floor Plan will continue for Grandfathered Employees
under the same formula as in effect prior to 1997 except that a Grandfathered
Employee's Floor Plan benefit will never be less than the value of the benefit
determined as of January 1, 1997 increased with interest. The benefit
distributed to Messrs. Lesar and Coleman was $0. The value of the
grandfathered Floor Plan benefits calculated as of December 31, 1998 for Mr.
Cheney is $0. The benefits for Mr. Cheney have been computed on the
assumptions that (i) payments will be paid in the form of a life annuity, (ii)
employment will continue until normal retirement at age 65, (iii) levels of
creditable compensation will remain constant, and (iv) offsetable defined
contribution allocations will average 7% of pay per year or more. Mr. Jones
has elected to take a lump sum retirement benefit of $115,917. Mr. LeSuer can
elect either a life annuity of $822 per month or a lump sum equal to $116,658.
 
                                      22
<PAGE>
 
  For Messrs. Bradford and Vaughn, the estimated total annual retirement
benefits payable under defined pension plans are set forth below:
 
Pension Plan Table
 
<TABLE>
<CAPTION>
                                         Years of Service
              ----------------------------------------------------------------------
Remuneration     5        10       15        20         25         30         35
- ------------  -------- -------- -------- ---------- ---------- ---------- ----------
<S>           <C>      <C>      <C>      <C>        <C>        <C>        <C>
 $1,000,000   $100,000 $200,000 $300,000 $  400,000 $  500,000 $  600,000 $  600,000
  1,150,000    115,000  230,000  345,000    460,000    575,000    690,000    690,000
  1,300,000    130,000  260,000  390,000    520,000    650,000    780,000    780,000
  1,450,000    145,000  290,000  435,000    580,000    725,000    870,000    870,000
  1,600,000    160,000  320,000  480,000    640,000    800,000    960,000    960,000
  1,800,000    180,000  360,000  540,000    720,000    900,000  1,080,000  1,080,000
  2,000,000    200,000  400,000  600,000    800,000  1,000,000  1,200,000  1,200,000
  2,200,000    220,000  440,000  660,000    880,000  1,100,000  1,320,000  1,320,000
  2,400,000    240,000  480,000  720,000    960,000  1,200,000  1,440,000  1,440,000
  2,600,000    260,000  520,000  780,000  1,040,000  1,300,000  1,560,000  1,560,000
  2,800,000    280,000  560,000  840,000  1,120,000  1,400,000  1,680,000  1,680,000
  3,000,000    300,000  600,000  900,000  1,200,000  1,500,000  1,800,000  1,800,000
  3,200,000    320,000  640,000  960,000  1,280,000  1,600,000  1,920,000  1,920,000
</TABLE>
 
  The gross amounts represented above include sums accrued under qualified and
non-qualified defined benefit plans. However, amounts credited to qualified
and non-qualified defined contribution plans will be paid from those plans and
thus represent deductions to the above gross amounts. Likewise, "pension
benefit equivalents" credited under Dresser's deferred compensation plan also
represent deductions. The benefit payable to Mr. Bradford is subject to a
special minimum calculation but, at this time, it is not anticipated that the
minimum will apply.
 
  The compensation used to determine pension benefits for Messrs. Bradford and
Vaughn is within 10% of the aggregate amounts shown in the salary and bonus
columns of the Summary Compensation Table. Years of credited service as of
December 31, 1998 used in determining benefits for these individuals are as
follows: Mr. Bradford, 35.42 years and Mr. Vaughn, 3.12 years. Benefits are
computed as straight-life annuity amounts which may be paid in various forms.
 
  In addition to the benefits described above for Mr. Vaughn, he is due an
additional $84,792 per year at age 65 from the defined benefit pension plan of
a Company subsidiary. This plan benefit is substantially frozen and does not
reflect future pay or service. The benefit is stated as a straight-life
annuity, but various other optional forms are available.
 
            EMPLOYMENT CONTRACTS AND TERMINATION OF EMPLOYMENT AND
                        CHANGE-IN-CONTROL ARRANGEMENTS
 
Employment Contracts
 
  Mr. Cheney entered into an employment agreement with the Company effective
August 10, 1995, which provided for his employment as Chairman of the Board
and Chief Executive Officer of the Company until September 30, 2003. (As of
the Effective Date of the Dresser Merger, and with Mr. Cheney's full
concurrence, Mr. Bradford was elected to succeed Mr. Cheney as Chairman of the
Board and Mr. Cheney retained his position as Chief Executive Officer.) Under
the agreement Mr. Cheney's cash compensation was specified for two periods,
the first being for the period from August 10, 1995 to December 31, 1995 and
the second, for the period beginning on January 1, 1996 and ending September
30, 2003. During the first period, Mr. Cheney received a salary, in the
aggregate, of $250,000; a bonus of $150,000, in lieu of participation in the
Company's Annual Performance Pay Plan; and a Supplemental Retirement Benefit
contribution of $125,000 under the SEDC Plan. During the second period, the
agreement provides that Mr. Cheney will receive an annual salary of not less
than $1,000,000; will participate in the Company's Annual Performance Pay Plan
beginning with the 1996 plan year; and will receive a Supplemental Retirement
Benefit contribution under the SEDC Plan of at least $500,000 annually. Also,
pursuant to the terms of the agreement, on August 10, 1995 Mr. Cheney was
granted a non-qualified stock option to purchase up to 400,000 shares of the
Company's Common Stock at $21.00 per share (the fair market value on such
date) and effective October 1, 1995 he was awarded 200,000 shares of Common
 
                                      23
<PAGE>
 
Stock subject to restrictions. (The foregoing share amounts and exercise price
have been adjusted to reflect the 2-for-1 stock split in 1997.) Both the stock
option grant and the restricted stock award were made under the 1993 Plan. The
employment agreement also provided for the Company to reimburse Mr. Cheney for
expenses associated with his relocation to Dallas.
 
  Under the terms of his employment agreement, in the event of Mr. Cheney's
termination for any reason other than his voluntary termination (as defined in
the agreement), death, disability or his termination by the Company for cause,
the Company is obligated to pay Mr. Cheney a severance payment consisting of a
lump sum cash payment equal to the value of any restricted shares that were
granted pursuant to the terms of the agreement and are forfeited because of
such termination of employment plus the lesser of (i) 150 percent of the base
salary that he would have received between the date of such termination of
employment and the end of the term of the agreement, or (ii) $3 million. Mr.
Cheney's continuing obligations to the Company after termination, including
non-competition obligations, are consideration for any severance payment that
may be made thereunder.
 
  Mr. Lesar entered into an employment agreement with the Company as of August
1, 1995 providing for his employment as Executive Vice President and Chief
Financial Officer of the Company. The agreement also provides that, while Mr.
Lesar is employed by the Company, management will recommend to the
Compensation Committee (i) annual supplemental retirement benefit allocations
under the SEDC Plan, and (ii) annual grants of stock options under the 1993
Plan. Such recommendations are to be consistent with the criteria utilized by
the Compensation Committee for similarly situated executives.
 
  Under the terms of his employment agreement, in the event Mr. Lesar is
involuntarily terminated by the Company for any reason other than termination
for cause (as defined in the agreement), the Company is obligated to pay Mr.
Lesar a severance payment equal to (i) the value of any restricted shares
granted under the 1993 Plan and that are forfeited because of such
termination, and (ii) five times his annual base salary.
 
  In addition, pursuant to the Agreement and Plan of Merger, dated as of
February 25, 1998 (the "Merger Agreement") relating to the Dresser Merger, the
Company entered into employment agreements with Messrs. Bradford and Vaughn
which became effective upon the Effective Date of the Dresser Merger.
Mr. Bradford became Chairman of the Company's Board of Directors and Mr.
Vaughn became Vice Chairman of the Company. Each of Messrs. Bradford and
Vaughn were also appointed to serve on the Company's Executive Committee along
with Messrs. Cheney and Lesar.
 
  The employment agreements provide that Mr. Bradford will serve as Chairman
of the Board and that Mr. Vaughn will serve as Vice Chairman of the Company.
The employment agreements further provide for (i) terms that commence at the
Effective Date and end, in the case of Mr. Bradford, on January 31, 2000 and,
in the case of Mr. Vaughn, on March 31, 2001, (ii) base salaries of $925,000
and $600,000 for Messrs. Bradford and Vaughn, respectively, (iii) payment to
each of the bonus earned by such individual under the Dresser 1998 Executive
Incentive Compensation Plan for the fiscal year ending October 31, 1998, as
well as a bonus calculated in the same manner as provided in such plan for the
two months ended December 31, 1998, (iv) participation by each in the
Halliburton Annual Performance Pay Plan commencing on January 1, 1999, subject
to a minimum equal to the average annual amount earned during fiscal years
1997 and 1998 under Dresser's incentive compensation plan, (v) participation
by each in the 1993 Plan, (vi) continued participation by each in Dresser's
Supplemental Executive Retirement Plan (to be adopted by the Company) and
(vii) participation by each in those other employee benefit plans made
generally available to executive employees of the Company. In addition, the
Company has in the employment agreements affirmed its obligations under the
Merger Agreement with respect to the Dresser employee benefit plans and, as a
consequence, the Company assumed the stock options held by Messrs. Bradford
and Vaughn and it honored the participation by each in the Dresser Deferred
Compensation Plan, the Dresser Performance Stock Unit Program, the Dresser
Executive Life Insurance Program, the Dresser Supplemental Executive
Retirement Plan, the Dresser Retirement Plan (in the case of Mr. Bradford) and
the M. W. Kellogg retirement plans (in the case of Mr. Vaughn) and the Dresser
Retiree Medical Benefit Plan. Under the employment agreements, each executive
will continue to receive all compensation and benefits provided
 
                                      24
<PAGE>
 
thereunder if his employment is terminated for any reason other than death, a
"voluntary termination" or for "cause" (as such terms are defined therein);
if, however, such executive's employment is terminated through death,
"voluntary termination" or "cause", he will be entitled to receive his base
salary pro rated through the date of termination, individual bonuses and
individual incentive compensation payable for prior years (but not for the
year of such termination) and benefits payable pursuant to the terms of
Dresser's and the Company's employee benefit plans (including any stock, stock
option, incentive compensation and deferred compensation plans). Each
executive is obligated under the employment agreement to refrain from
competing with the Company for one year after termination of employment.
 
  Mr. Coleman entered into an employment agreement with the Company effective
September 29, 1998, providing for his employment as Executive Vice President
and General Counsel of the Company. The employment agreement further provides
that Mr. Coleman will receive an annual base salary of not less than $450,000
and will participate in the Company's Annual Performance Pay Plan. Also,
pursuant to the agreement, Mr. Coleman was granted an award under the 1993
Plan of 15,000 shares of Common Stock subject to restrictions.
 
  Under the terms of his employment agreement, in the event of Mr. Coleman's
termination for any reason other than his voluntary termination (as defined in
the agreement), death, permanent disability, retirement (either at or after
age 65 or voluntarily at his election prior to such age), or his termination
by the Company for cause (as defined in the agreement), the Company is
obligated to pay Mr. Coleman a severance payment consisting of a lump sum cash
payment equal to (i) the value of any restricted shares that were forfeited
because of such termination; (ii) two years' base salary and (iii) any unpaid
bonus earned in prior years. In addition, Mr. Coleman will also be entitled to
receive any bonus payable for the year in which his employment is terminated
determined as if he had remained employed for the full year.
 
Arrangements Relating to Executive Officer Retirements
 
  Mr. Jones retired as Vice Chairman of the Company on October 2, 1998 and
resigned as a member of the Company's Board of Directors and the Executive
Committee on September 29, 1998, the Effective Date of the Dresser Merger,
after more than 33 years of service. On September 29, 1998, the Company and
Mr. Jones entered into an agreement relating to the terms of his early
retirement and consulting services to be performed following his retirement.
In connection with Mr. Jones' early retirement, the Company agreed to make a
supplemental retirement benefit contribution in the amount set forth in
footnote (6) to the Summary Compensation Table. Further, Mr. Jones agreed to
provide consulting services from the period beginning October 2, 1998 through
September 30, 2000 and to forbear, during such period, from certain activities
detrimental to the Company. In consideration of the foregoing, the Company
agreed to pay Mr. Jones consulting fees of $20,834 per month until September
30, 2000 and a monthly allowance of $1,750 for office space and secretarial
support over the same period. In addition, as a result of Mr. Jones'
retirement, restrictions lapsed on 29,800 shares of Common Stock awarded under
the Career Executive Incentive Stock Plan (the "Career Plan") and the 1993
Plan. The fair market value of such shares on October 2, 1998 was $826,245.
 
  On September 29, 1998, the Effective Date of the Dresser Merger, Mr. LeSuer
resigned as Vice Chairman of the Company and as a member of the Executive
Committee of the Company. He subsequently took early retirement from the
Company on January 1, 1999 after almost 40 years of service. On September 29,
1998, the Company and Mr. LeSuer entered into an agreement relating to the
terms of his continued employment until January 1, 1999 and consulting
services to be performed following his retirement. In consideration of his
continued employment through January 1, 1999, the Company agreed to continue
his salary at the current rate and to make a supplemental retirement benefit
contribution in the amount set forth in footnote (6) to the Summary
Compensation Table. In addition, Mr. LeSuer agreed to provide consulting
services from the period beginning January 2, 1999 through December 31, 2000
and to forbear, during such period, from certain activities
 
                                      25
<PAGE>
 
detrimental to the Company. In consideration thereof, the Company agreed to
pay Mr. LeSuer consulting fees of $20,834 per month until December 31, 2000
and a monthly allowance of $1,750 for office space and secretarial support
over the same period. As a result of Mr. LeSuer's retirement, restrictions
lapsed on 19,900 shares of Common Stock under the Career Plan and the 1993
Plan. The fair market value of such shares on January 1, 1999 was $589,660.
 
Change-In-Control Arrangements
 
  Pursuant to the 1993 Plan, in the event of a change-in-control:
 
  A. The Compensation Committee, acting in its sole discretion, will act to
effect one or more of the following alternatives with respect to outstanding
stock options: (i) accelerate the time at which options may be exercised; (ii)
cancel the options and pay the Optionees the excess of the per share value
offered to stockholders in the change-in-control transaction over the exercise
price(s) of the shares subject to options; (iii) make adjustments to the
options as deemed appropriate to reflect the change-in-control; or (iv)
convert the options to rights to purchase a proportionate amount of shares of
stock or other securities or property paid to stockholders in the change-in-
control transaction.
 
  B. The Compensation Committee may, with respect to outstanding restricted
stock, provide for full vesting of all shares of restricted stock and
termination of all restrictions applicable thereto.
 
  Pursuant to the Career Plan, the Compensation Committee may, in the event of
a tender offer for all or a part of the Company's Common Stock, accelerate the
lapse of restrictions on any or all shares on which restrictions have not
theretofore lapsed.
 
  Under the Annual Performance Pay Plan, in the event of a change-in-control,
a participant will be entitled to an immediate cash payment equal to the
maximum amount he or she would have been entitled to for such year prorated
through the date of the change-in-control and all deferred amounts earned in
prior years shall be paid in cash immediately.
 
                CERTAIN RELATIONSHIPS AND RELATED TRANSACTIONS
 
  Dresser has outstanding approximately $6.1 million in letters of credit
under a bank facility which was established in connection with certain
insurance relationships of NL Industries, Inc. ("NL"), of which Mr. Martin is
a director and executive officer. NL is obligated to indemnify Dresser for any
losses or expenses in respect of these letters of credit.
 
      DIRECTORS' COMPENSATION, RESTRICTED STOCK PLAN AND RETIREMENT PLAN
 
 Directors' Fees and Deferred Compensation Plan
 
  All non-employee Directors of the Company receive an annual fee of $30,000
and an attendance fee of $2,000 for each meeting of the Board of Directors.
Such Directors also receive an attendance fee of $2,000 per meeting for
Committee service. The Chairmen of the Audit; Compensation; Nominating and
Corporate Governance; Health, Safety and Environment; and Management Oversight
Committees each receive an additional $2,000 annually for service in such
capacities. Under the Company's Directors' Deferred Compensation Plan,
Directors are permitted to defer their fees, or a portion thereof, until after
they cease to be a Director of the Company. A participant may elect, on a
prospective basis, to have his or her deferred compensation account either
credited quarterly with interest at the prime rate of Citibank, N.A. or
translated on a quarterly basis into Company Common Stock equivalents.
Distribution will be made in cash either in a lump sum or in annual
installments over a 5- or 10-year period, as determined by the committee
appointed to administer the Plan in its discretion. Ms. Armstrong and Messrs.
Crandall, DiBona, Eagleburger, Hunt, Precourt and Stegemeier have elected to
participate in the Plan.
 
                                      26
<PAGE>
 
 Directors' Restricted Stock Plan
 
  Pursuant to the terms of the Restricted Stock Plan for Non-Employee
Directors ("Directors' Restricted Stock Plan"), which was approved by the
stockholders at the 1993 Annual Meeting, each non-employee Director receives
an annual award of 400 restricted shares of Common Stock as a part of his or
her compensation. The awards are in addition to the Directors' annual retainer
and attendance fees and to amounts that would be payable under the Directors'
Retirement Plan, described below. Shares awarded under the Directors'
Restricted Stock Plan may not be sold, assigned, pledged or otherwise
transferred or encumbered until the restrictions are removed. Restrictions
will be removed following termination of Board service under certain
circumstances, which include, among others, death or disability, retirement
pursuant to the Company's mandatory retirement policy, or early retirement
after at least four years of service. During the restriction period, Directors
have the right to vote and to receive dividends with respect to the restricted
shares. Any shares which, pursuant to such Plan's provisions, remain
restricted following termination of service will be forfeited.
 
 Directors' Retirement Plan
 
  Under the terms of the Retirement Plan for Directors of the Company
("Directors' Retirement Plan"), a non-employee Director participant upon the
benefit commencement date (the later of a participant's termination date or
attainment of age 65) will receive an annual benefit equal to the last annual
retainer for such participant for a period of years equal to such
participant's years of service on his or her termination date; provided that a
minimum benefit payment period for each participant is 5 years. Non-employee
Directors become participants in the Directors' Retirement Plan upon the
completion of three years of service, as defined in such Plan. Upon the death
of a participant, benefit payments will be made to the surviving spouse, if
any, over the remainder of the retirement benefit payment period. Years of
service for each Director participant under the Plan are: Ms. Armstrong--22,
Lord Clitheroe--12, Mr. Crandall--14, Mr. Howell--8, Mr. Lewis--3, Mr. Silas--
6 and Mr. Stegemeier--5. Assets of the Company are transferred to Chase Bank
of Texas, as Trustee, to be held pursuant to the terms of an irrevocable
grantor trust to aid the Company in meeting its obligations under the
Directors' Retirement Plan. The corpus and income of the trust are treated as
assets and income of the Company for federal income tax purposes and are
subject to the claims of general creditors of the Company to the extent
provided therein.
 
            PROPOSAL FOR RATIFICATION OF THE SELECTION OF AUDITORS
 
                                   (Item 2)
 
  Arthur Andersen LLP has examined the financial statements of the Company
since 1946. A resolution will be presented at the Annual Meeting to ratify the
appointment by the Board of Directors of the Company of that firm as
independent accountants to examine the financial statements and the books and
records of the Company for the year ending December 31, 1999. Such appointment
was made upon the recommendation of the Audit Committee. The Company has been
advised by Arthur Andersen LLP that neither the firm nor any member thereof
has any direct financial interest or any material indirect interest in the
Company and, during at least the past three years, neither such firm nor any
member thereof has had any connection with the Company in the capacity of
promoter, underwriter, voting trustee, Director, officer or employee.
 
  Representatives of such firm are expected to be present at the Annual
Meeting, will have an opportunity to make a statement if they desire to do so
and are expected to be available to respond to appropriate questions from
stockholders.
 
  The affirmative vote of the holders of a majority of the shares of the
Company's Common Stock represented at the Annual Meeting and entitled to vote
on the matter is needed to approve the proposal.
 
  If the stockholders do not ratify the selection of Arthur Andersen LLP, the
selection of independent accountants will be reconsidered by the Board of
Directors.
 
  The Board of Directors recommends a vote FOR ratification of the appointment
of Arthur Andersen LLP as independent accountants to examine the financial
statements and books and records of the Company for the year 1999.
 
                                      27
<PAGE>
 
                             COST OF SOLICITATION
 
  Officers and other employees of the Company may solicit proxies personally,
by telephone, facsimile or other electronic communications, from some
stockholders if proxies are not received promptly. The Company will reimburse
banks, brokers or other persons holding Company Common Stock in their names or
in the names of their nominees for their charges and expenses in forwarding
proxies and proxy material to beneficial owners of the Company's Common Stock.
All expenses of solicitation of proxies will be borne by the Company. In
addition, Georgeson & Company Inc. has been retained to assist in the
solicitation of proxies for the 1999 Annual Meeting of Stockholders at a fee
of $11,000 plus reasonable expenses.
 
               STOCKHOLDER PROPOSALS FOR THE 2000 ANNUAL MEETING
 
  Stockholders are entitled to submit proposals on matters appropriate for
stockholder action consistent with regulations of the Securities and Exchange
Commission. Should a stockholder intend to present a proposal at the 2000
Annual Meeting, it must be received by the Secretary of the Company (3600
Lincoln Plaza, 500 N. Akard Street, Dallas, Texas 75201-3391) not later than
November 26, 1999 and must comply with all of the requirements of Rule 14a-8
under the Securities Exchange Act of 1934, as amended, in order to be included
in the Company's Proxy Statement and form of proxy relating to that meeting.
The 2000 Annual Meeting of Stockholders will be held May 16, 2000.
 
                                OTHER BUSINESS
 
  The Company's By-laws provide that in addition to any other applicable
requirements, for business to be properly brought before the Annual Meeting by
a stockholder, the stockholder must give timely notice in writing to the
Secretary. To be timely, a stockholder's notice must be delivered to or mailed
and received at the principal executive offices of the Company, not less than
ninety (90) days prior to the anniversary date of the immediately preceding
stockholders meeting. A stockholder's notice to the Secretary shall set forth
as to each matter the stockholder proposes to bring before the Annual Meeting
(i) a brief description of the business desired to be brought before the
Annual Meeting and the reasons for conducting such business at the Annual
Meeting, (ii) the name and record address of the stockholder proposing such
business, (iii) the class and number of shares of the Company which are
beneficially owned by the stockholder, (iv) a representation that the
stockholder or a qualified representative of the stockholder intends to appear
in person to bring the proposed business before the Annual Meeting, and (v)
any material interest of the stockholder in such business. This requirement
does not preclude discussion by any stockholder of any business properly
brought before the Annual Meeting in accordance with such procedures.
 
  The management of the Company is not aware of any business to come before
the meeting other than those matters described above in this Proxy Statement.
If any other matters should properly come before the meeting, however, it is
intended that proxies in the accompanying form will be voted in respect
thereof in accordance with the judgment of the person or persons voting the
proxies.
 
                                              By Authority of the Board of
                                                        Directors,
 
                                                   /s/ SUSAN S. KEITH
                                                     Susan S. Keith
                                              Vice President and Secretary
 
March 25, 1999
 
                                      28
<PAGE>
 
PROXY

                              HALLIBURTON COMPANY

                 Proxy for 1999 Annual Meeting of Stockholders
          This Proxy is solicited on behalf of the Board of Directors

      The undersigned hereby appoints  W.E. Bradford, R.B. Cheney and S.S. 
Keith, and any of them, proxies or proxy with full power of substitution and 
revocation as to each of them, to represent the undersigned and to act and vote,
with all powers which the undersigned would possess if personally present, at 
the Annual Meeting of Stockholders of Halliburton Company to be held in the 
Horchow Auditorium of the Dallas Museum of Art, 1717 North Harwood Street, 
Dallas, Texas, on Tuesday, May 18, 1999, on the following matters and in their 
discretion on any other matters which may come before the meeting or any 
adjournments thereof. Receipt of Notice-Proxy Statement dated March 25, 1999, is
acknowledged.


                 (Continued and to be signed on reverse side)


                            [FOLD AND DETACH HERE]

<PAGE>
 
To vote in accordance with the Board of Directors' recommendations just sign
below; no boxes need to be checked. The Board of Directors Recommends a Vote FOR
Items 1 and 2.


Please mark
your votes as
indicated in         X
this example



Item 1--Election of Directors

   FOR all nominees                              WITHHOLD
  listed to the right                            AUTHORITY
(except as marked to the                 to vote for all nominees
contrary)                                   listed to the right

(Instruction: To withhold authority to vote for an individual nominee write that
nominee's name on the space provided below)

Nominees: 01 Anne L. Armstrong, 02 W.E. Bradford, 03 R.B. Cheney, 04 Lord 
Clitheroe, 05 R.L. Crandall, 06 C.J. DiBona, 07 L.S. Eagleburger, 08 W.R. 
Howell, 09 R.L. Hunt, 10 D.E. Lewis, 11 J.L. Martin, 12 J.A. Precourt, 13 C.J. 
Silas and 14 R.J. Stegemeier.

- --------------------------------------------------------------------------------


Item 2--Proposal for ratification of selection of independent public accountants
for the Company for 1999.

   FOR   AGAINST   ABSTAIN
   [_]     [_]       [_]


Item 3--In their discretion, upon such other business as may properly come 
before the meeting.

This proxy when properly executed will be voted in the manner directed herein by
the undersigned.

In the absence of such direction the proxy will be voted FOR the nominees listed
in Item 1 and FOR the Proposal set forth in Item 2.


I PLAN TO ATTEND THE MEETING


Signature__________________________ Signature__________________________ Date____
NOTE:  Please sign as name appears hereon. Joint owners should each sign. When 
signing as attorney, executor, administrator, trustee or guardian, please give 
full title as such.

                            [FOLD AND DETACH HERE]

                               VOTE BY TELEPHONE
                         QUICK *** EASY *** IMMEDIATE

           YOUR VOTE IS IMPORTANT!--YOU CAN VOTE IN ONE OF TWO WAYS:
 1. TO VOTE BY PHONE: Call toll-free 1-800-840-1208 on a touch tone telephone 
                          24 hours a day-7days a week
   There is NO CHARGE to you for this call. - Have your proxy card in hand.
     You will be asked to enter a Control Number, which is located in the 
               box in the  lower right hand corner of this form
- --------------------------------------------------------------------------------
OPTION 1: To vote as the Board of Directors recommends on ALL proposals, press 1
- --------------------------------------------------------------------------------
                   When asked, please confirm by Pressing 1.
- --------------------------------------------------------------------------------
OPTION 2: If you choose to vote on each Proposal separately, press 0. You will 
          hear these instructions:
- --------------------------------------------------------------------------------
          Proposal 1 - To vote FOR ALL nominees, press 1; to WITHHOLD FOR ALL
          nominees, press 9; To WITHHOLD FOR AN INDIVIDUAL nominee, Press 0 and
          listen to the instructions

          Proposal 2 - To vote FOR, press 1; AGAINST, press 9; ABSTAIN, press 0.

                   When asked, please confirm by Pressing 1.

                                      or
                                      --

2. TO VOTE BY PROXY: Mark, sign and date your proxy card and return promptly in 
                     the enclosed envelope.

         NOTE: if you vote by telephone, THERE IS NO NEED TO MAIL BACK
                               your Proxy Card.

                             THANK YOU FOR VOTING.


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