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)

                           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




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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  May 7, 1997, registrant issued a press release entitled
Halliburton  $50 Million Notes Offering pertaining,  among  other
things,  to  an  announcement  that an offering  of  $50  million
principal  amount  7.53  percent notes due  May  12,  2017  under
registrant's medium-term note program was issued on May  7,  1997
through registrant's agents. The notes were priced at par.

      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 May 7, 1997.












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

























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                          EXHIBIT INDEX



Exhibit                                           Sequentially
Number              Description                   Numbered Page

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































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FOR IMMEDIATE RELEASE          Contact-Guy T. Marcus
May 7, 1997                            Vice President-Inv. Rel.
                                       (214) 978-2691

           HALLIBURTON $50 MILLION NOTES OFFERING

     DALLAS, Texas -- An offering of $50 million principal amount
Halliburton Company (NYSE-HAL) 7.53 percent notes due May 12,
2017 under the company's medium-term note program was issued
today through the company's agents Merrill Lynch & Co., Lehman
Brothers, Morgan Stanley & Co. Incorporated and NationsBanc
Capital Markets, Inc. The notes were priced at par.

     The net proceeds from the sale of the notes will be added to
Halliburton's general funds and used for general corporate
purposes which may include repayment of debt, acquisitions, and
loans and advances to and/or investments in subsidiaries of
Halliburton to support their requirements for working capital,
repayment of debt and capital expenditures.

     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.

                         # # #

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