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 High Income
         Fund, a series of Scudder High Income Series, 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.


December 2, 2005                     /s/Vincent J. Esposito
                                     -------------------------
                                     Vincent J. Esposito
                                     President
                                     Scudder High Income Fund, a series of
                                     Scudder High Income Series












                                                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 High Income
         Fund, a series of Scudder High Income Series, 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.

December 2, 2005             /s/Paul Schubert
                             ---------------------
                             Paul Schubert
                             Chief Financial Officer and Treasurer
                             Scudder High Income Fund, a series of Scudder High
                             Income Series