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 7, 1997

                       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


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 7, 1997, registrant issued a press release entitled
Halliburton Purchases Minority Interest in PES pertaining,  among
other  things, to an announcement that a subsidiary of registrant
purchased  a  26%  ownership interest  in  Petroleum  Engineering

      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

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 7, 1997.

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


      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 7,1997                By: /s/ Susan S. Keith
                                     Susan S. Keith
                                     Vice President, Secretary and
                                     Corporate Counsel

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

                          EXHIBIT INDEX

Exhibit                                             Sequentially
Number                 Description                  Numbered Page

    20                 Press Release of
                       May 7, 1997                     5 of 5
                       Incorporated by Reference

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

FOR IMMEDIATE RELEASE                Contacts
                                     Media:              Brandon Lackey
                                                         (713) 624-3483

                                     Investor Relations: Guy Marcus
                                                         (214) 978-2691


HOUSTON,  Texas (May 7, 1997) - Halliburton Energy  Services and Petroleum
Engineering Services (PES) announced today the purchase by Halliburton of a
26% ownership interest in  PES. This  development is a further
strengthening of the alliance between  the two organizations announced last
September  for the  development and delivery of intelligent well completion
systems.    Sometimes  called  "smart  wells,"   these   new completions
can help oil and gas companies reduce  operating expenditures   and
enhance  hydrocarbon  recovery   through improved reservoir management.

       Zeke   Zeringue,  president  of  Halliburton   Energy Services,
said, "This investment by Halliburton helps assure alignment with PES in
our cooperative effort to continue  to bring leading-edge technologies to
the emerging intelligent well  market.   We  believe that smart well
technology  will revolutionize  well  completions in the industry  and
we're pleased  to  be strengthening our relationship with  PES  to provide
the preferred solution to our customers."

      "This  relationship also gives us the  opportunity  to integrate
another   component  into  Halliburton's   broad completion  product
offerings,"  added  Zeringue,  "further strengthening our capabilities in
this important area."

      "This  investment is a major step forward for the  PES group," said
Larry Kinch, chairman of PES.  "It will provide the financial   platform
and   access   to   the   global infrastructure  we  need to expand our
business  worldwide." Kinch went on to say that, by integrating
technologies  and services,  Halliburton and PES are positioned to offer
"the world's  premier  solution for surface controlled  reservoir
monitoring and management of multilateral wells."

       Headquartered   in   Aberdeen,  Scotland,   Petroleum Engineering
Services  is a leading provider  of  specialist well  completions  and
intervention products,  services  and solutions.   Since  its founding in
1986,  the  company  has grown its  revenues to over 16 million British
pounds  and employs more than 230 people.

     Halliburton Energy Services Inc., a Halliburton Company organization
(NYSE:HAL), is a leading supplier of  products, services and integrated
solutions to the energy industry  on a global basis.

                             #    #    #

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