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 6, 1999

                        SOUTHWEST SECURITIES GROUP, INC.
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             (Exact name of Registrant as specified in its charter)


       DELAWARE                  No. 0-19483    No. 75-2040825

(State or other jurisdicition    (Commission   (IRS employer
of incorporation)                File Number)  Identification No.)
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                        SOUTHWEST SECURITIES GROUP, INC.
                          1201 ELM STREET, SUITE 3500
                              DALLAS, TEXAS  75270
          (Address, including zip code, of principal executive office)
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       Registrants' telephone number, including area code:  214-859-1800


                                 Not applicable
                            -----------------------
          (Registrant's former address of principal executive office)


Item 5.   OTHER EVENTS

     On June 6, 1999, the Registrant entered into a letter of intent to acquire
100 percent of the outstanding shares of ASBI Holdings, Inc. ("ASBI"), the
holding company for First Savings Bank FSB, Arlington, Texas.  The letter of
intent provides that the Registrant will issue 2.6 million shares of its common
stock in exchange for all of the outstanding stock of ASBI Holdings, Inc.

     Don A. Buchholz serves as chairman of both the Registrant and ASBI, and is
the beneficial owner of approximately 9.0% of the Registrant's outstanding
voting securities.  Mr. Buchholz is the beneficial owner of approximately 50% of
the outstanding voting securities of ASBI, and exercises voting control for
approximately 88% of such securities.

     Consummation of the acquisition is subject to due diligence, negotiation of
a definitive agreement, and corporate, regulatory and shareholder approvals.


Item 7. FINANCIAL STATEMENTS AND EXHIBITS.

(c) Exhibits. Exhibit 99.  Southwest Securities Group, Inc. Press Release issued
June 6, 1999.



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.



                    SOUTHWEST SECURITIES GROUP, INC.
                    Date: June 7, 1999



                    By: /s/ David Glatstein
                        -----------------------------------------
                            David Glatstein
                            President and Chief Executive Officer


                                 EXHIBIT INDEX



EXHIBIT NO.        DESCRIPTION OF EXHIBIT

99                 Southwest Securities Group, Inc. Press Release
                   Issued June 6, 1999