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                       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) APRIL 29, 1996


                    NATIONAL CONVENIENCE STORES INCORPORATED
               (Exact Name of Registrant as Specified in Charter)



    DELAWARE                        1-7936                      74-1361734
   (State of                      (Commission                  (IRS Employer
 Incorporation)                  File Number)               Identification No.)



      9830 COLONNADE BOULEVARD, SAN ANTONIO, TEXAS             78230
        (Address of Principal Executive Offices)             (Zip Code)

      Registrant's telephone number, including area code:  (210) 641-6800



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ITEM 5.  OTHER EVENTS.

         As previously reported in its Quarterly Report on Form 10-Q for the
period ended December 31, 1995, National Convenience Stores Incorporated (the
"Company") was merged with a wholly owned subsidiary of Diamond Shamrock, Inc.
("Diamond Shamrock") on December 18, 1995 (the "Merger").  As a result of the
Merger and pursuant to the terms of the Warrant Agreement, dated March 9, 1993
(the "Warrant Agreement"), between the Company and Boatmen's Trust Company as
warrant agent (the "Warrant Agent"), each outstanding warrant to purchase
shares of the Company's common stock, par value $.01 per share (the
"Warrants"), represents the right to receive $27.00 per Warrant in cash (the
"Warrant Payment") upon payment of the $17.75 exercise price (the "Exercise
Price"), in lieu of the one share of the Company's common stock previously
issuable upon exercise of a Warrant.

         Pursuant to the terms of an Escrow Trust Agreement, dated April 29,
1996 (the "Escrow Agreement"), between the Company and the Warrant Agent, the
Company has deposited $293,687.50 in cash (the "Funds") with the Warrant Agent
to pay the $9.25 difference between the Warrant Payment and the Exercise Price
(the "Spread") for all outstanding Warrants.  The Funds will be held in escrow
pursuant to the Escrow Agreement for the benefit of, and payment to, the record
holders of the Warrants.  On May 6, 1996, the Company provided written notice
to the record Warrant holders of the deposit of the Funds and the right to
receive payment of the Spread upon exercise of the Warrants.  A copy of that
notice has been filed as an exhibit to this report and is incorporated herein
by this reference.  The Warrants will expire at 5:00 p.m., New York City time,
on March 9, 1998 (the "Expiration Time"), after which time the balance of the
Funds, if any, will be returned to the Company.  Each Warrant not exercised
prior to the Expiration Time will automatically become void and no longer
outstanding.

         Based upon a letter from the Securities and Exchange Commission in
response to a no-action request filed by the Company, the Company will cease to
file periodic reports pursuant to Sections 13 and 15(d) of the Securities
Exchange Act of 1934, as amended.


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

         (c) EXHIBITS


                   
             99.1 --  Notice to holders of outstanding Warrants of the Company






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                                   SIGNATURES


         Pursuant to the requirements of the Securities Exchange Act of 1934,
the Company has duly caused this report to be signed on its behalf by the
undersigned hereunto duly authorized.


                                      NATIONAL CONVENIENCE STORES INCORPORATED



                                      By: /s/ TIMOTHY J. FRETTHOLD           
                                          -----------------------------------
                                          Timothy J. Fretthold
                                          Senior Vice President


Date:  May 7, 1996





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                              INDEX TO EHXIBITS

EXHIBIT 
NUMBER                           DESCRIPTION
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   99.1    --    Notice to holders of outstanding Warrants of the Company





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