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)

                                  JULY 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




                                Page 1 of 6 Pages
                       The Exhibit Index Appears on Page 4






         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 July 2, 1997,  registrant  issued a press release  entitled  Brown &
Root Wins North Sea Contract For Amerada Hess pertaining, among other things, to
an announcement that registrant's  wholly-owned subsidiary,  Brown & Root Energy
Services, has been awarded a facilities contract,  valued at almost $300 million
for Amerada Hess' South Arne field development in the Danish sector of the North
Sea.

         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 July 2, 1997.












                                Page 2 of 6 Pages
                       The Exhibit Index Appears on Page 4






                                   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: July 2, 1997                            By:  /s/ Susan S. Keith
                                                 ----------------------------
                                                   Susan S. Keith
                                                   Vice President, Secretary and
                                                   Corporate Counsel

























                                Page 3 of 6 Pages
                       The Exhibit Index Appears on Page 4






                                  EXHIBIT INDEX



Exhibit                                                        Sequentially
Number                         Description                     Numbered Page

    20                         Press Release of
                               July 2, 1997                         5 of 6
                               Incorporated by Reference































                                Page 4 of 6 Pages
                       The Exhibit Index Appears on Page 4