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                                  UNITED STATES
                       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 13, 1998


                          TESORO PETROLEUM CORPORATION
             (Exact name of registrant as specified in its charter)



                                                                                      
               DELAWARE                              1-3473                          95-0862768
    (State or other jurisdiction of                (Commission                    (I.R.S. Employer
            incorporation)                        File Number)                   Identification No.)




                8700 TESORO DRIVE, SAN ANTONIO, TEXAS 78217-6218
               (Address of principal executive offices) (Zip Code)



        Registrant's telephone number, including area code: 210-828-8484

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ITEM 5.           OTHER EVENTS

As previously reported, on March 18, 1998, Tesoro Petroleum Corporation
("Tesoro", the "Company" or the "Registrant") entered into a stock sale
agreement ("Hawaii Stock Sale Agreement") to purchase (the "Hawaii Acquisition")
all of the outstanding stock of two subsidiaries of The Broken Hill Proprietary
Company Limited ("BHP") (together, "BHP Hawaii"). BHP Hawaii owns and operates a
95,000-barrel per day refinery in Kapolei, Hawaii, on the island of Oahu,
approximately 20 miles west of Honolulu, and 32 retail gasoline stations on the
islands of Oahu, Maui and Hawaii. The cash purchase price for the Hawaii
Acquisition is currently estimated to be approximately $275 million. The cash
purchase price will be adjusted after closing for the amount by which the
working capital of BHP Hawaii differs from $100 million at the closing date. In
addition, Tesoro will issue an unsecured, non-interest bearing promissory note
(the "BHP Note") in the amount of $50 million, payable in five equal annual
installments of $10 million each, beginning on the eleventh anniversary date of
the closing. The BHP Note provides for earlier payment based on the financial
performance of BHP Hawaii.

The Hawaii Acquisition is scheduled to close on May 29, 1998.


ITEM 7.           FINANCIAL STATEMENTS, PRO FORMA FINANCIAL INFORMATION 
                  AND EXHIBITS

                  (a)    FINANCIAL STATEMENTS OF BUSINESS ACQUIRED.

                         Included as Exhibit 99.1 to this Form 8-K are the
                         audited combined balance sheets of BHP Petroleum
                         Americas Refining Inc. and BHP Petroleum South Pacific
                         Inc. as of May 31, 1997 and 1996 and the related
                         combined statements of operations, stockholders' equity
                         and cash flows for each of the three years in the
                         period ended May 31, 1997. Included as Exhibit 99.2 to
                         this Form 8-K are the unaudited combined balance sheets
                         of BHP Petroleum Americas Refining Inc. and BHP
                         Petroleum South Pacific Inc. as of December 31, 1997
                         and 1996 and the related combined statements of
                         operations and cash flows for the seven months then
                         ended.

                  (b)    PRO FORMA FINANCIAL INFORMATION.

                         Included as Exhibit 99.3 of this Form 8-K is the
                         unaudited pro forma combined condensed financial
                         statements of the Company and BHP Petroleum Americas
                         Refining Inc. and BHP Petroleum South Pacific Inc. as 
                         of and for the year ended December 31, 1997.

                  (c)    EXHIBITS

                  *2.1   Stock Sale Agreement, dated March 18, 1998, among the
                         Company, BHP Hawaii Inc. and BHP Petroleum Pacific 
                         Islands Inc.

                 +23.1   Consent of Arthur Andersen LLP.

                 +99.1   Audited Combined Financial Statements of BHP Petroleum
                         Americas Refining Inc. and BHP Petroleum South Pacific
                         Inc. as of May 31, 1997 and 1996.

                 +99.2   Unaudited Combined Financial Statements of BHP
                         Petroleum Americas Refining Inc. and BHP Petroleum
                         South Pacific Inc. as of December 31, 1997 and 1996.

                 +99.3   Pro Forma Combined Condensed Financial Statements of
                         the Company and BHP Petroleum Americas Refining Inc.
                         and BHP Petroleum South Pacific Inc. as of and for the
                         year ended December 31, 1997. 

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*  Previously filed.
+  Filed herewith.




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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.


                                            TESORO PETROLEUM CORPORATION
                                                      REGISTRANT




Date: May 13, 1998                      By: /s/ BRUCE A. SMITH
                                           -----------------------------------
                                           Bruce A. Smith
                                           Chairman of the Board of Directors,
                                           President and Chief Executive Officer


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                                  EXHIBIT INDEX


EXHIBIT                            DESCRIPTION
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    *2.1               Stock Sale Agreement, dated March 18, 1998, among the
                       Company, BHP Hawaii Inc. and BHP Petroleum Pacific
                       Islands Inc.

   +23.1               Consent of Arthur Andersen LLP.

   +99.1               Audited Combined Financial Statements of BHP Petroleum
                       Americas Refining Inc. and BHP Petroleum South Pacific
                       Inc. as of May 31, 1997 and 1996.

   +99.2               Unaudited Combined Financial Statements of BHP Petroleum
                       Americas Refining Inc. and BHP Petroleum South Pacific
                       Inc. as of December 31, 1997 and 1996.

   +99.3               Pro Forma Combined Condensed Financial Statements of the
                       Company and BHP Petroleum Americas Refining Inc. and BHP
                       Petroleum South Pacific Inc. as of and for the year ended
                       December 31, 1997.

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*  Previously filed.
+  Filed herewith.


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