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 24, 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






                                Page 1 of 6 Pages
                       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 May 24, 1999 registrant issued a press release entitled "Halliburton's Brown & Root Services Wins State Department Contract pertaining, among other things, to an announcement that registrant's Brown & Root Services business unit has been awarded a contract by the U.S. Department of State to perform fast track delivery of security improvements at up to 150 U.S. embassies and consulates throughout the world. The two year contract with one additional option year is valued at up to $100 million. 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 24, 1999. Page 2 of 6 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 6 Pages The Exhibit Index Appears on Page 4

EXHIBIT INDEX Exhibit Sequentially Number Description Numbered Page 20 Press Release of 5 of 6 May 24, 1999 Incorporated by Reference Page 4 of 6 Pages The Exhibit Index Appears on Page 4


FOR IMMEDIATE RELEASE                  CONTACT: Wendy Hall Nantz
(May 24, 1999)                                  Public Relations
                                                Halliburton Company
                                                (713) 676-5227
                                                wendy.hall.nantz@halliburton.com


HALLIBURTON'S BROWN & ROOT SERVICES WINS STATE DEPARTMENT CONTRACT

BRS Will Upgrade Up To 150 United States Embassies and Consulates Throughout the
World

DALLAS,  Texas - Brown & Root Services  (BRS),  a business  unit of  Halliburton
Company (NYSE: HAL), has been awarded a contract by the U.S. Department of State
to perform fast track delivery of security  improvements  at U.S.  embassies and
consulates  throughout  the world.  The two year  contract  with one  additional
option year,  valued at up to $100  million,  requires  BRS to perform  physical
security and technical  security systems  surveys,  followed by detailed design,
construction  and  installation  of improved  systems  for up to 150  facilities
throughout the world.
         The  contract  will  require  simultaneous  survey  and  small  capital
construction  work  at a  multitude  of  international  locations.  Brown & Root
Services  will  provide  the  equipment,  people,  communication  and  technical
expertise  to execute  security/infrastructure  improvements  at each  location.
Security upgrade plans for 50 state department  locations are already  underway.
Brown & Root Services began the contract April 23, 1999.
         "Brown & Root Services will capitalize on Halliburton's global presence
and established infrastructure in more than 130 countries throughout the world,"
said Dave Lesar,  president,  Halliburton Company.  "This will benefit the State
Department by leveraging established local resources and business relationships,
backed by a network of worldwide Halliburton Company offices."


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"This practice of business enables Brown & Root Services to provide our best value solutions for the State Department's needs because we have the people and skills to plan and execute multiple projects, each of which represents complex challenges," said Randy Harl, president, Brown & Root Services. The competition for the contract included eight companies bidding for the work. Brown & Root Services and Perini Corporation were the companies selected to execute the security upgrades. Other companies that competed for the contract included: Morrison Knudsen, JA Jones Construction, Turner International, Bechtel, Bill Harbert International Construction and Fluor Daniel. Brown & Root Services, a 20,000 employee global company, operates in the Americas, UK, Europe, Africa and Asia-Pacific. Brown & Root Services specializes in comprehensive facilities engineering, design, development, construction, logistics, operations and maintenance. This work is performed for private sector and government clients in simultaneous multiple domestic and international locations. Halliburton Company is the world's leading diversified energy services, engineering, energy equipment, construction and maintenance companies. Founded in 1919, Halliburton provides a broad range of energy services and products, industrial and marine engineering and construction services. In 1998, Halliburton's consolidated revenues were $17.4 billion and it conducted business with a workforce of approximately 100,000 in more than 130 countries. The company's World Wide Web site can be accessed at http://www.halliburton.com. ### Page 6 of 6 Pages The Exhibit Index Appears on Page 4