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 6, 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






                                Page 1 of 7 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 May 6, 1996,  registrant issued a press release entitled Halliburton
Installs   World's  First   Multi-Lateral   System  With  Full  Re-Entry  Access
pertaining, among other things, to an announcement that registrant's Halliburton
Energy  Services  business  segment has  successfully  installed a multi-lateral
system with full lateral liner connectivity,  a  hydraulically-isolated  lateral
junction and full-bore lateral re-entry access.  The system is the world's first
to provide  full-bore  re-entry  access to the  lateral  while  maintaining  the
integrity of the main wellbore.  The multi-lateral system was installed in Norsk
Hydro's Oseberg field. The successful installation of this system is viewed as a
technical breakthrough by Norsk Hydro and registrant.

         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 6, 1996
                  ----------











                                Page 2 of 7 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:    May 6, 1996                                 By: _______________________
                                                         Robert M. Kennedy
                                                         Vice President - Legal





























                                Page 3 of 7 pages
                       The Exhibit Index appears on Page 4

                                  EXHIBIT INDEX



Exhibit                                                            Sequentially
Number                     Description                             Numbered Page
- -------                    -----------                             -------------
  20                       Press Release of
                           May 6, 1996                                5 of 7
                           Incorporated by Reference






























                                Page 4 of 7 pages
                       The Exhibit Index appears on Page 4