Exhibit 32.1


           CERTIFICATION PURSUANT TO 18 U.S.C. SECTION 1350 AS ADOPTED
            PURSUANT TO SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002


      The undersigned hereby certify that the Quarterly Report on Form 10-Q for
the quarter ended June 25, 2004 filed by Ameritrade Holding Corporation with the
Securities and Exchange Commission fully complies with the requirements of
Section 13(a) or 15(d) of the Securities Exchange Act of 1934 and that
information contained in the report fairly presents, in all material respects,
the financial condition and results of operations of the issuer.

Dated: August 3, 2004               /s/ Joseph H. Moglia
                                    -----------------------------------------
                                    Joseph H. Moglia
                                    Chief Executive Officer

Dated: August 3, 2004               /s/ John R. MacDonald
                                    -----------------------------------------
                                    John R. MacDonald
                                    Executive Vice President, Chief Financial
                                        Officer and Treasurer