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)

                          JUNE 2, 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 June 2, 1997, registrant issued a press release entitled
Brown  & Root Awarded Army Sustainment Contract pertaining, among
other  things, to an announcement  that registrant's wholly-owned
business  unit,  Brown  &  Root Energy  Services,  will  continue
logistics  support  services through the  duration  of  Operation
Joint  Guard  in the Balkans.  The U.S. Army awarded  the  $137.9
million  contract  through  May 1998 with  two  six-month  option
periods,  which  would  bring the total contract  value  to  $270
million.

      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 June 2, 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: June 2, 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
                      June 2, 1997                     5 of 6
                      Incorporated by Reference































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