

                       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 7, 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






                                Page 1 of 5 Pages
                       The Exhibit Index Appears on Page 4
<PAGE>

         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 7, 1998 registrant issued a press release entitled  Halliburton
 Awarded Well Services Contract by Phillips Petroleum Norway  pertaining,  among
 other things, to an announcement that Halliburton AS, the Norwegian division of
 registrant's  Halliburton  Energy  Services  business  unit, has been awarded a
 contract to provide Phillips  Petroleum Norway with zonal isolation and pumping
 services  for the  entire  Ekofisk  field area in the North  Sea.  The  initial
 contract is for a  five-year  period and  includes an option for an  additional
 five years.

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 7, 1998.






                                Page 2 of 5 Pages
                       The Exhibit Index Appears on Page 4

<PAGE>


                                   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 14, 1998               By: /s/ Susan S. Keith
                                        ----------------------------------
                                             Susan S. Keith
                                             Vice President and Secretary







                                Page 3 of 5 Pages
                       The Exhibit Index Appears on Page 4

<PAGE>

                                  EXHIBIT INDEX


Exhibit                                                       Sequentially
Number                     Description                        Numbered Page

20                         Press Release of                   5 of 5
                           July 7, 1998
                           Incorporated by Reference






                                Page 4 of 5 Pages
                       The Exhibit Index Appears on Page 4
