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
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


     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

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                The Exhibit Index appears on Page 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

FOR IMMEDIATE RELEASE              Contact - Guy T. Marcus
May 20, 1994                        Vice President-Inv. Rel.
                                    (214) 978-2691


DALLAS, Texas -- Halliburton Company has elected Richard J.
Stegemeier, chairman of Unocal Corporation, to serve as a
member of its board of directors.  Mr. Stegemeier was elected
at Halliburton's annual shareholders meeting on May 17, 1994.

Mr. Stegemeier, 65, has been with Unocal since 1951, when he
joined the company's principal operating subsidiary, Union Oil
Company of California.  He served as Unocal Corporation's
chief executive officer from July 1988 until his retirement on
May 1, 1994 and has served as chairman of the company since
April 1989.

In addition to serving on the Halliburton board of directors
he is a director of Unocal Corporation, First Interstate
Bancorp, Foundation Health Corporation, Northrop Corporation
and Outboard Marine Corporation.
Mr. Stegemeier also serves as the chairman of the California
Chamber of Commerce and the Los Angeles World Affairs Council,
and he is a member of the National Academy of Engineering, the
Council on Foreign Relations, the Advisory Board of the US
Secretary of Energy, The Conference Board and the California
Council on Science and Technology.

A native of Illinois, Mr. Stegemeier earned his BS degree in
petroleum engineering from the University of Missouri-Rolla in
1950 and his MS degree, also in petroleum engineering, from
Texas A&M University in 1951.

Halliburton Company is one of the world's largest diversified
energy services, engineering, maintenance and construction
companies.  In 1994 Halliburton is celebrating 75 years of
providing customers with a broad range of energy services and
products, industrial and marine engineering and construction
services, and property and casualty insurance services.

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