

                       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 12, 1998

                               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 12, 1998 registrant issued a press release entitled Halliburton
 Renotification   Effective  Date   pertaining,   among  other  things,   to  an
 announcement that following further contacts with the European Commission,  the
 renotification became complete on June 3, 1998 with the result that the initial
 one-month  review  period  provided for under the European  Community's  merger
 regulation will in principle expire on July 6, 1998.

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 12, 1998.







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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 23, 1998                By:
                                         ----------------------------------
                                         Susan S. Keith
                                         Vice President and Secretary







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                                  EXHIBIT INDEX



Exhibit                                                       Sequentially
Number                     Description                        Numbered Page

20                         Press Release of                   5 of 5
                           June 12, 1998
                           Incorporated by Reference





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