
               SECURITIES AND EXCHANGE COMMISSION

                     Washington, D.C. 20549



                            FORM 8-K

                         CURRENT REPORT

             PURSUANT TO SECTION 13 OR 15(d) OF THE
                 SECURITIES EXCHANGE ACT OF 1934

        DATE OF REPORT (date of earliest event reported)

                           MAY 7, 1997

                       Halliburton Company
     (Exact name of registrant as specified in its charter)

State or other           Commission          IRS Employer
jurisdiction             File Number         Identification
of incorporation                             Number

Delaware                    1-3492           No. 75-2677995

                       3600 Lincoln Plaza
                     500 North Akard Street
                    Dallas, Texas 75201-3391
            (Address of principal executive offices)

                 Registrant's telephone  number,
               including area code - 214/978-2600




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     INFORMATION TO BE INCLUDED IN REPORT

Item 5.   Other Events

      The  registrant may, at its option, report under this  item
any  events,  with respect to which information is not  otherwise
called  for by this form, that the registrant deems of importance
to security holders.

      On  May 7, 1997, registrant issued a press release entitled
Halliburton Purchases Minority Interest in PES pertaining,  among
other  things, to an announcement that a subsidiary of registrant
purchased  a  26%  ownership interest  in  Petroleum  Engineering
Services.

      The  foregoing summary is subject to the full text  of  the
press  release with respect thereto, a copy of which is  attached
hereto  as  Exhibit 20, which exhibit is incorporated  herein  by
reference.

Item 7.   Financial Statements and Exhibits

      List  below  the financial statements, pro forma  financial
information and exhibits, if any, filed as part of this report.

     (c)  Exhibits.

          Exhibit 20 - Press release dated May 7, 1997.
















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                           SIGNATURES

      Pursuant to the requirements of the Securities Exchange Act
of  1934, the registrant has duly caused this report to be signed
on its behalf by the undersigned hereunto duly authorized.


                                 HALLIBURTON COMPANY




Date:  May 7,1997                By: /s/ Susan S. Keith
                                     -----------------------------
                                     Susan S. Keith
                                     Vice President, Secretary and
                                     Corporate Counsel

























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                          EXHIBIT INDEX



Exhibit                                             Sequentially
Number                 Description                  Numbered Page

    20                 Press Release of
                       May 7, 1997                     5 of 5
                       Incorporated by Reference































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