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



President
Section 906 Certification under Sarbanes Oxley Act





I, Vincent J. Esposito, certify that:

1.       I have reviewed this report, filed on behalf of Scudder Money Market
         Series (Premium Shares and Prime Reserve Shares), a series of Scudder
         Money Market Trust, on Form N-CSR;

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 23, 2006             /s/Vincent J. Esposito
                             ---------------------------
                             Vincent J. Esposito
                             President
                             Scudder Money Market Series (Premium Shares and
                             Prime Reserve Shares), a series of Scudder Money
                             Market Trust









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


Chief Financial Officer and Treasurer
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 (Premium Shares and Prime Reserve Shares), a series of Scudder
         Money Market Trust, on Form N-CSR;

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 23, 2006             /s/Paul Schubert
                             ---------------------------
                             Paul Schubert
                             Chief Financial Officer and Treasurer
                             Scudder Money Market Series (Premium Shares and
                             Prime Reserve Shares), a series of Scudder Money
                             Market Trust