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 18, 1999

                               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  18,  1999   registrant   issued  a  press   release   entitled
 "Halliburton's   1999  Shareholders'   Meeting  and  Second  Quarter  Dividend"
 pertaining,  among  other  things,  to an  announcement  that the  registrant's
 stockholders  have elected all fourteen  nominees to the board of directors and
 ratified  the  appointment  of Arthur  Andersen  LLP to audit the  registrant's
 financial  statements for 1999 and that the registrant's board of directors has
 declared a 1999 second quarter  dividend of 12.5 cents a share on  registrant's
 common stock,  payable June 24, 1999 to  shareholders of record at the close of
 business on June 3, 1999.

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 18, 1999.




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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 18, 1999                  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 18, 1999
                           Incorporated by Reference





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FOR IMMEDIATE RELEASE               Contact: Guy T. Marcus
May 18, 1999                                 Vice President-Investor Relations
                                             214/978-2691


               HALLIBURTON'S 1999 SHAREHOLDERS' MEETING AND SECOND
                                QUARTER DIVIDEND

         DALLAS,  Texas - At Halliburton  Company's (NYSE:HAL) annual meeting of
shareholders in Dallas today, the shareholders  elected all fourteen nominees to
the board of directors and ratified the  appointment  of Arthur  Andersen LLP to
audit the company's financial statements for the year 1999.
         At the board of directors' meeting following the shareholders' meeting,
the board  declared  a second  quarter  dividend  of 12.5 cents per share on the
common stock,  payable June 24, 1999 to  shareholders  of record at the close of
business on June 3, 1999.
         Halliburton  Company,  founded in 1919, is the world's largest provider
of products and services to the  petroleum  and energy  industries.  The company
serves its  customers  with a broad range of products and  services  through its
Energy Services Group,  Engineering and Construction Group and Dresser Equipment
Group business  segments.  The company's  World Wide Web site can be accessed at
http://www.halliburton.com.
                                       ###


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