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)

                               DECEMBER 23, 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. 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
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     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 December 23, 1996, registrant issued a press release entitled
Halliburton Acknowledges Potential Acquisition pertaining, among other things,
to an announcement that registrant acknowledged that it is in discussions with
OGC International plc concerning a possible acquisition of OGC by 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 December 23, 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:  December 27, 1996                By: /s/ DAVID J. LESAR
                                           ------------------------------
                                              David J. Lesar
                                              Executive Vice President and
                                              Chief Financial Officer



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                                 EXHIBIT INDEX



Exhibit                                                       Sequentially
Number                     Description                        Numbered Page
- ------                     -----------                        -------------

  20                      Press Release of
                          December 23, 1996                      
                          Incorporated by Reference              5 of 5



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                                  Exhibit 20




FOR IMMEDIATE RELEASE                   Contact -- Steve Moore
- ---------------------                              Investor Relations
December 23,1996                                   (214) 978-2696

                HALLIBURTON ACKNOWLEDGES POTENTIAL ACQUISITION
                ----------------------------------------------

    DALLAS, Texas -- Halliburton Company (NYSE: HAL)acknowledges that it is in
discussions with OGC International plc, a U.K. company traded on the London
Stock Exchange, concerning a possible acquisition by Halliburton of OGC. OGC
and Halliburton announced these discussions earlier today in the U.K.

    OGC provides a variety of engineering, operations and maintenance services
to the petroleum industry, primarily in the North Sea.  In 1995 it had revenues
of 233 million U.K. Pounds ($385 million) and pre-tax profit of 14.2 million
U.K. Pounds ($23.5 million).  For the first six months ended June 30, 1996, OGC
had revenues of 91 million U.K. Pounds ($150 million) and pre-tax profit of 2.7
million U.K. Pounds ($4.5 million).  As of June 30, 1996, OGC had total
shareholders' equity of 37 million U.K. Pounds ($61 million).  

    Halliburton Company is one of the world's largest diversified energy
services, engineering, maintenance, and construction companies.  Halliburton
provides a broad range of energy services and products, industrial and marine
engineering and construction services.

    A further announcement will be made when appropriate.


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