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 17, 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

                         Page 1 of 6 pages
                The Exhibit Index appears on Page 4
                INFORMATION TO BE INCLUDED IN REPORT
  2
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 20, 1994, the registrant issued a press release
entitled Halliburton
Elects Stegemeier New Director pertaining, among other things, to
the election of
Richard J. Stegemeier as a member of its Board of Directors.

     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 20, 1994.

                         Page 2 of 6 pages
                The Exhibit Index appears on Page 4
  3

                             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 3, 1994               By:(Robert M. Kennedy)
                                        ----------------------
                                        Robert M. Kennedy
                                        Vice President - Legal

                         Page 3 of 6 pages
                The Exhibit Index appears on Page 4

  4
                           EXHIBIT INDEX

Exhibit                                      Sequentially
Number              Description                   Numbered Page

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

                         Page 4 of 6 pages
                The Exhibit Index appears on Page 4