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                                                                    EXHIBIT 99.1

 
PROXY

                              HALLIBURTON COMPANY

  PROXY FOR 1998 SPECIAL MEETING, IN LIEU OF ANNUAL MEETING, OF STOCKHOLDERS
          THIS PROXY IS SOLICITED ON BEHALF OF THE BOARD OF DIRECTORS

    The undersigned hereby appoints R.B. Cheney, D.P. Jones 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 
Special Meeting of Stockholders of Halliburton Company to be held at The Plaza
Ballroom, Le Meridien Dallas Hotel, 650 North Pearl Street, Dallas, Texas, at
9:00 a.m. on June 25, 1998, 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-Joint Proxy Statement/Prospectus dated _____________, 1998, is
acknowledged.

                 (Continued and to be signed on reverse side)

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                                                        Please mark      
                                                        your votes as [X]
                                                        indicated in     
                                                        this example      


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, 2, 3 AND 4.

Item 1-Proposal to amend               Item 2-Proposal to issue shares of 
Certificate of Incorporation to        Common Stock pursuant to the       
increase authorized Common Stock.      Agreement and Plan of Merger       
                                       among the Company, a wholly owned
                                       subsidiary of the Company and      
FOR       AGAINST         ABSTAIN      Dresser Industries, Inc.            
[ ]         [ ]             [ ]    

                                         FOR       AGAINST       ABSTAIN  
                                         [ ]         [ ]           [ ]     
                    
Item 3-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: Anne L. Armstrong, R.B. Cheney, Lord Clitheroe, R.L. Crandall, C.J. 
DiBona, W.R. Howell, D.P. Jones, D.E. Lewis, C.J. Silas, and R.J. Stegemeier.

Item 4-Proposal for ratification of selection of independent public accountants
for the Company for 1998.

                    FOR       AGAINST       ABSTAIN  
                    [ ]         [ ]           [ ]     

Item 5-In their discretion, upon such other business incident to the conduct of
the meeting as may properly come before the meeting.

THIS PROXY WHEN PROPERLY EXECUTED WILL BE VOTED IN THE 
MANNER DIRECTED HEREIN BY THE UNDERSIGNED.
                                                                 I PLAN TO    
IN THE ABSENCE OF SUCH DIRECTION THE PROXY WILL BE VOTED          ATTEND      
FOR THE NOMINEES LISTED IN ITEM 3 AND FOR THE PROPOSALS            THE    [ ] 
SET FORTH IN ITEMS 1,2 AND 4.                                    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.

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