[Letterhead of Vinson & Elkins L.L.P.]

                                                                 Exhibit 8.2

                            September 13, 1999





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

          Subject: PES (International) Limited
          ------------------------------------

Gentlemen:

     We participated in the preparation of the Registration Statement on Form S-
4 with respect to the Recommended Offer by Halliburton Company for the Ordinary
Share Capital of PES (International) Limited, including the discussion set forth
in the Registration Statement under the heading "United States Federal Tax
Consequences."

     We hereby affirm that the discussion and the legal conclusions with respect
to the United States federal tax matters set forth herein constitute our opinion
as to the material United States federal tax consequences of the Offer and the
Compulsory Acquisition to holders of PES Shares.

     We hereby consent to the use of our name in the Registration Statement and
to the filing of this opinion as part of the Registration Statement.


                              Very truly yours,



                              VINSON & ELKINS L.L.P.