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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 Act of 1934

         Date of Report (Date of earliest event reported) June 25, 1998



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



    Delaware                         1-3473                      95-0862768
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   (State or other                 (Commission                 (IRS Employer
   jurisdiction of                 File Number)              Identification No.)
   incorporation)


8700 Tesoro Drive, San Antonio, Texas                                   78217
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(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.

         On June 25, 1998, Tesoro Petroleum Corporation (the "Company") entered
into (a) an Underwriting Agreement with Lehman Brothers Inc. and Howard, Weil,
Labouisse, Friedrichs Incorporated, pursuant to which the Company issued
9,000,000 Premium Income Equity Securities ("PIES"), each of which represents
one one-hundredth of a share of Mandatorily Convertible Preferred Stock of the
Company deposited with The Bank of New York, and (ii) an Underwriting Agreement
with Lehman Brothers Inc., CIBC Oppenheimer, Credit Suisse First Boston, Merrill
Lynch & Co. and Salomon Smith Barney for 5,000,000 shares of Common Stock of the
Company. The proceeds of the issuance of the PIES and Common Stock, together
with borrowings under the Company's senior credit facility, will be used to fund
the cash purchase price of the acquisition of Shell Anacortes Refining Company,
to refinance the Company's interim credit facility (a portion of which was used
to fund the cash purchase price of the acquisition of the Company's Hawaii
operations), to pay certain fees and expenses and for general corporate purposes
(including working capital requirements and capital expenditures).



Item 7.           Financial Statements and Exhibits.

         (c)      Exhibits.

         Exhibit 1.1       Premium Income Equity Securities Underwriting 
                           Agreement dated June 25, 1998.

         Exhibit 1.2       Common Stock Underwriting Agreement dated June 25, 
                           1998.

         Exhibit 4.1       Certificate of Designation related to the Mandatorily
                           Convertible Preferred Stock.

         Exhibit 4.2       Deposit Agreement among the Company, The Bank of
                           New York and the holders from time to time of
                           depository receipts executed and delivered
                           thereunder.

         Exhibit 4.3       Form of depository receipt evidencing ownership
                           of Premium Income Equity Securities (filed as a part
                           of Exhibit 4.2 hereof).

         Exhibit 5.1       Opinion of Fulbright & Jaworski L.L.P.

         Exhibit 23.1      Consent of Fulbright & Jaworski L.L.P. (included in 
                           Exhibit 5.1).






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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 thereunto duly authorized.

                                         TESORO PETROLEUM CORPORATION


                                          By: /s/ James C. Reed, Jr.
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                                                  James C. Reed, Jr.
                                                  Executive Vice President,
                                                  General Counsel and Secretary


DATE:  July 1, 1998



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                                 EXHIBIT INDEX


Exhibit 1.1       Premium Income Equity Securities Underwriting Agreement dated 
                  June 25, 1998.

Exhibit 1.2       Common Stock Underwriting Agreement dated June 25, 1998.

Exhibit 4.1       Certificate of Designation related to the Mandatorily 
                  Convertible Preferred Stock.

Exhibit 4.2       Deposit Agreement among the Company, The Bank of New York
                  and the holders from time to time of depository receipts
                  executed and delivered thereunder.

Exhibit 4.3       Form of depository receipt evidencing ownership of Premium
                  Income Equity Securities (filed as part of Exhibit 4.2 
                  hereof).

Exhibit 5.1       Opinion of Fulbright & Jaworski L.L.P.

Exhibit 23.1      Consent of Fulbright & Jaworski L.L.P. (included in Exhibit 
                  5.1).