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 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 6, 2004                                   /s/Julian Sluyters
                                                   Julian Sluyters
                                                   Chief Executive Officer
                                                   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
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 6, 2004                               /s/Paul Schubert
                                               Paul Schubert
                                               Chief Financial Officer
                                               Scudder High Income Fund, a
                                               series of Scudder High Income
                                               Series