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, 2002

                               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 5 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 June 4, 2002 registrant issued a press release entitled "Halliburton Asbestos Plaintiffs Agree to Extend Current Stay on Asbestos Claims," pertaining to an announcement that registrant has reached agreement with Harbison-Walker Refractories Company and the Official Committee of Asbestos Creditors in the Harbison-Walker bankruptcy to consensually extend the period of the stay contained in the Bankruptcy Court's temporary restraining order until July 16, 2002. The Committee also informed the Court that further 30-day extensions are anticipated as long as negotiations proceed in a constructive manner. The Court's temporary restraining order originally entered on February 14, 2002 stays more than 200,000 pending asbestos claims against registrant's subsidiary, Dresser Industries, Inc. See registrant's earlier press releases of May 20, 2002, February 22, 2002 and February 14, 2002 for more details on the stay entered by the Court on February 14, 2002 and extended on February 21 and April 4, 2002. 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, 2002. 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 4, 2002 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, 2002 Incorporated by Reference Page 4 of 5 Pages The Exhibit Index Appears on Page 4


FOR IMMEDIATE RELEASE               Contact:  Cedric Burgher
- ---------------------                         Vice President, Investor Relations
June 4, 2002                                  713-676-4608

                                              Wendy Hall
                                              Manager, Media Relations
                                              713-676-5227


HALLIBURTON ASBESTOS PLAINTIFFS AGREE TO EXTEND CURRENT STAY ON ASBESTOS CLAIMS

Dallas,  Texas - Halliburton  Company  (NYSE:  HAL) today  announced that it has
reached  agreement with  Harbison-Walker  Refractories  Company and the Official
Committee  of  Asbestos   Creditors  in  the   Harbison-Walker   bankruptcy   to
consensually  extend the period of the stay contained in the Bankruptcy  Court's
temporary restraining order until July 16, 2002. The Committee also informed the
court that further  30-day  extensions are  anticipated as long as  negotiations
proceed in a constructive manner. The Court's temporary restraining order, which
was  originally  entered on February 14, 2002,  stays more than 200,000  pending
asbestos claims against  Halliburton's  subsidiary Dresser Industries,  Inc. For
more  details on the stay  entered by the Court on February  14, and extended on
February 21 and April 4, Halliburton refers to its earlier press releases of May
20, 2002, February 22, 2002 and February 14, 2002.

Halliburton,  founded  in  1919,  is one of the  world's  largest  providers  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 and Engineering and  Construction  Group business  segments.  The
company's World Wide Web site can be accessed at www.halliburton.com.



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