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






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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 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.






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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:    July 14, 1998               By: /s/ Susan S. Keith
                                        ----------------------------------
                                             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
                           July 7, 1998
                           Incorporated by Reference






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FOR IMMEDIATE RELEASE           Contact:  Julia Humphreys
July 7, 1998                              Public Relations
                                          Halliburton Company
                                          (713) 676-3875


                   HALLIBURTON AWARDED WELL SERVICES CONTRACT
                          BY PHILLIPS PETROLEUM NORWAY

DALLAS, Texas -- Halliburton AS, the Norwegian division of Halliburton Company's
(NYSE:  HAL)  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.

         The work will be managed from Halliburton's Tananger, Norway office and
will involve approximately 50 employees.  Engineering,  procurement of materials
and equipment,  offshore  operations and laboratory services are all included in
the agreement. The purchase of goods and services from local Norwegian companies
will account for roughly 60% of the value of the contract.

         "Halliburton  is  dedicated  to  technological  leadership,  as well as
operational  excellence,  and I believe this focus is  reflected by  Halliburton
being awarded this  contract,"  said Dave Lesar,  president and chief  operating
officer,   Halliburton  Company.  "During  our  20-year  history  with  Phillips
Petroleum  Norway, we have developed a strong alliance.  Halliburton  values its
relationship  with  Phillips,  and we look  forward to  working  on the  Ekofisk
project."

         Halliburton  Company is one of the world's largest  diversified  energy
services, engineering,  maintenance and construction companies. Founded in 1919,
Halliburton  provides a broad range of energy services and products,  industrial
and marine  engineering and construction  services.  Halliburton Energy Services
provides   products,   services  and  integrated   solutions  for  oil  and  gas
exploration,  development  and  production.  Halliburton AS currently  employs a
staff of more  than  1,250 in  Norway.  The  company  has been  involved  in the
Norwegian petroleum industry for more than 25 years.

                                       ###

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