Deutsche Asset Management [LOGO]
                                             A Member of the Deutsche Bank Group



Chief Executive Officer
Section 906 Certification under Sarbanes Oxley Act






I, Julian Sluyters, certify that:

1.   I have reviewed this report, filed on behalf of Scudder Money Market
     Series, a series of Scudder Money Market Trust, on Form N-CSR of the
     Scudder Money Market Series (the "Company");

2.   Based on my knowledge and pursuant to 18 U.S.C. ss. 1350, the periodic
     report on Form N-CSR (the "Report") fully complies with the requirements of
     ss. 13 (a) or ss. 15 (d), as applicable, of the Securities Exchange Act of
     1934 and that the information contained in the Report fairly presents, in
     all material respects, the financial condition and results of operations of
     the Company.




January 31, 2005                             /s/Julian Sluyters
                                             Julian Sluyters
                                             Chief Executive Officer
                                             Scudder Money Market Series, a
                                             series of Scudder Money Market
                                             Trust



                                             Deutsche Asset Management [LOGO]
                                             A Member of the Deutsche Bank Group



Chief Financial Officer
Section 906 Certification under Sarbanes Oxley Act






I, Paul Schubert, certify that:

1.   I have reviewed this report, filed on behalf of Scudder Money Market
     Series, a series of Scudder Money Market Trust, on Form N-CSR of the
     Scudder Money Market Series (the "Company");

2.   Based on my knowledge and pursuant to 18 U.S.C. ss. 1350, the periodic
     report on Form N-CSR (the "Report") fully complies with the requirements of
     ss. 13 (a) or ss. 15 (d), as applicable, of the Securities Exchange Act of
     1934 and that the information contained in the Report fairly presents, in
     all material respects, the financial condition and results of operations of
     the Company.




January 31, 2005                             /s/Paul Schubert
                                             Paul Schubert
                                             Chief Financial Officer
                                             Scudder Money Market Series, a
                                             series of Scudder Money Market
                                             Trust