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







Chief Executive Officer
Section 906 Certification under Sarbanes Oxley Act





I, Richard T. Hale, 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.




May 28, 2004                                     /sRichard T. Hale/
                                                 Richard T. Hale
                                                 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, Charles A. Rizzo, 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.




May 28, 2004                                      /s/Charles A. Rizzo
                                                  Charles A. Rizzo
                                                  Chief Financial Officer
                                                  Scudder High Income Fund, a
                                                  series of Scudder High Income
                                                  Series