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 21, 1994

                        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. 73-0271280

                         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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                The Exhibit Index appears on Page 4
                INFORMATION TO BE INCLUDED IN REPORT
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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 21, 1994, the registrant issued a press release entitled Shell
Launches Massive Coiled-Tubing Drilling Program -- Halliburton Drilling 68
Wells -- pertaining, among other things, to a coiled-tubing drilling program
with Halliburton Energy Services for injection wells in a California field.

     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 June 21, 1994.

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                The Exhibit Index appears on Page 4

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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 29, 1994                 By: (Robert M. Kennedy)
                                             Robert M. Kennedy
                                           Vice President - Legal

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                The Exhibit Index appears on Page 4

 4
                           EXHIBIT INDEX



Exhibit                                           Sequentially
Number              Description                   Numbered Page

    20              Press Release of
                    June 21, 1994                   5-6 of 6
                    Incorporated by Reference

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                The Exhibit Index appears on Page 4