Exhibit 8.1



(713) 758-2192                                                    (713) 615-5210


                                 May 15, 1998


Halliburton Company
3600 Lincoln Plaza
500 North Akard Street
Dallas, Texas 75201-3391


Gentlemen:

     You have requested our opinion with respect to certain federal income tax 
consequences under the Internal Revenue Code of 1986, as amended (the "Code") of
the merger of Halliburton N.C., Inc. ("Merger Sub"), a Delaware corporation and 
a wholly-owned subsidiary of Halliburton Company ("Halliburton"), a Delaware 
corporation, with and into Dresser Industries, Inc. ("Dresser"), a Delaware 
corporation (the "Merger").

     Our opinion is based upon (i) the Agreement and Plan of Merger, dated as of
February 25, 1998, by and among Halliburton, Merger Sub and Dresser (the "Merger
Agreement")/1/, including the representations contained therein, (ii) the facts 
set forth in the Registration Statement filed with the Securities and Exchange 
Commission with respect to the Merger, and (iii) current provisions of the Code,
existing regulations thereunder, current administrative rulings of the Internal 
Revenue Service and court decisions. Based thereupon, and conditioned upon our 
assumption that the transactions contemplated by the Merger Agreement will be 
carried out strictly in accordance with the terms of the Merger Agreement, it is
our opinion that:

            (i)    the Merger will constitute a reorganization under section 
     368(a) of the Code;

            (ii)   Halliburton, Merger Sub and Dresser will each be a party to
     that reorganization within the meaning of section 368(b) of the Code; and

            (iii)  no gain or loss will be recognized by Halliburton, Merger Sub
     or Dresser by reason of the Merger.


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     /1/ Capitalized terms used but not defined herein have the meanings
         ascribed to them in the Merger Agreement.






 
Halliburton Company
Page 2
May 15, 1998

        We participated in the preparation of the Registration Statement. We 
hereby confirm that the conclusions of law with respect to federal income tax 
matters set forth in the Registration Statement under the heading "Certain 
Federal Income Tax Consequences" are accurate and complete in all material 
respects.

        We hereby consent to the use of our name in the Registration Statement 
and to the filing of this letter as an exhibit to the Registration Statement.


                                       Very truly yours,


                                       VINSON & ELKINS L.L.P.