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 4, 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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                       The Exhibit Index Appears on Page 4

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 June 4, 1999 registrant issued a press release entitled Halliburton Files Registration Statement to Cover Shares to Acquire Remainder of PES pertaining, among other things, to an announcement that registrant filed a Form S-4 registration statement with the Securities and Exchange Commission covering 3,069,899 shares of registrant's common stock. Registrant plans to utilize up to 3,069,899 shares of the common stock as consideration to acquire all of the ordinary shares of PES (International) Limited ("PES") not already owned by a subsidiary of registrant or about 74 percent of PES. A subsidiary of registrant currently owns about 26 percent of the ordinary shares of PES. The offering will be made only by means of an offer document constituting a part of the registration statement when it is declared effective. 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 4, 1999. Page 2 of 5 Pages The Exhibit Index Appears on Page 4

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 7, 1999 By: /s/ Susan S. Keith --------------------------------- Susan S. Keith Vice President and Secretary Page 3 of 5 Pages The Exhibit Index Appears on Page 4

EXHIBIT INDEX Exhibit Sequentially Number Description Numbered Page 20 Press Release of 5 of 5 June 4, 1999 Incorporated by Reference Page 4 of 5 Pages The Exhibit Index Appears on Page 4



FOR IMMEDIATE RELEASE      Contact: Guy T. Marcus
June 4, 1999                        Vice President-Investor Relations
                                    214/978-2691

          HALLIBURTON FILES REGISTRATION STATEMENT TO COVER SHARES TO
                            ACQUIRE REMAINDER OF PES


         DALLAS,  Texas -- Halliburton Company (NYSE:HAL) today filed a Form S-4
registration  statement  with the Securities  and Exchange  Commission  covering
3,069,899 shares of the company's common stock.
         Halliburton  plans to utilize up to the 3,069,899  shares of the common
stock covered by the  registration  statement as consideration to acquire all of
the ordinary shares of PES (International)  Limited (PES) not already owned by a
subsidiary  of  Halliburton,  or  about  74  percent  of PES.  A  subsidiary  of
Halliburton currently owns about 26 percent of the ordinary shares of PES.
         The  offering  will  be  made  only  by  means  of  an  offer  document
constituting a part of the registration statement when it is declared effective.
          The core business of PES,  headquartered  in Scotland,  is the design,
manufacture and supply of oil and gas well completion and intervention products,
services and solutions.
         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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