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)

                                  APRIL 8, 1996

                               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. 73-0271280

                               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 April 8, 1996,  registrant  issued a press release entitled Alliance
Starts on  BP's 400 Million (pounds sterling) Schiehallion Project pertaining,  
among  other  things,  to  an  announcement  that  an  alliance  involving  BP, 
registrant's Brown & Root subsidiary,  Harland and Wolff,  Single Buoy  Moorings
and  Coflexip Stena Offshore  has now started  work on  the 400  million (pounds
sterling) contract to design and build the surface production  facility for BP's
Schiehallion  Field. Up to 3,500 jobs  across  Europe  will be created  by  the
contract award. Registrant's subsidiary, Brown & Root, will have responsibility
for project  management, the design  and fabrication of the FPSO's topsides and
for the vessel installation.

         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 April 8, 1996
















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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:    April 10, 1996                         By: _______________________
                                                       Robert M. Kennedy
                                                       Vice President - Legal





























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                                  EXHIBIT INDEX



Exhibit                                                          Sequentially
Number                          Description                      Numbered Page

  20                            Press Release of
                                April 8, 1996                      5 of 6
                                Incorporated by Reference
































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