EXHIBIT 32.1

      CERTIFICATION OF CO-CHIEF EXECUTIVE OFFICERS UNDER 18 U.S.C. Section 1350

         We, William R. Cruz and Ralph L. Cruz, Co-Chairmen of the Board and
Co-Chief Executive Officers of TradeStation Group, Inc., hereby certify, to our
respective knowledge, that:

         The Annual Report on Form 10-K of TradeStation Group, Inc. for the year
ended December 31, 2003 (the "Report") fully complies with the requirements of
Section 13(a) or 15(d), as applicable, of the Securities Exchange Act of 1934
and the information contained in the Report fairly presents, in all material
respects, the financial condition and results of operations of TradeStation
Group, Inc.

         The foregoing certification is being furnished solely pursuant to 18
U.S.C. Section 1350 and is not being filed as part of the Report or as a
separate disclosure document.

March 12, 2004                     /s/ William R. Cruz
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Date                               William R. Cruz
                                   Co-Chairman of the Board
                                      and Co-Chief Executive Officer

March 12, 2004                     /s/ Ralph L. Cruz
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Date                               Ralph L. Cruz
                                   Co-Chairman of the Board
                                      and Co-Chief Executive Officer