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 19, 1998

                               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 19, 1998 registrant issued a press release entitled  Halliburton
 Second Quarter Dividend pertaining, among other things, to an announcement that
 registrant's  board of directors has declared a 1998 second quarter dividend of
 12.5 cents a share on  registrant's  common  stock,  payable  June 24,  1998 to
 shareholders of record at the close of business on June 3, 1998.

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 19, 1998.



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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 19, 1998                By: /s/  Susan S. Keith
                                         -----------------------------
                                              Susan S. Keith
                                              Vice President and Secretary



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                                  EXHIBIT INDEX


Exhibit                                                       Sequentially
Number                     Description                        Numbered Page

20                         Press Release of                   5 of 5
                           May 19, 1998
                           Incorporated by Reference




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FOR IMMEDIATE RELEASE                       Contact: Guy T. Marcus
May 19, 1998                                         V.P.-Investor Relations
                                                     (214) 978-2691


                       HALLIBURTON SECOND QUARTER DIVIDEND


         DALLAS,  Texas -- Halliburton  Company (NYSE:HAL)  announced today that
its board of directors has declared a 1998 second quarter dividend of 12.5 cents
a share on the company's common stock,  payable June 24, 1998 to shareholders of
record at the close of business on June 3, 1998.
         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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