Deustche Asset Management [LOGO]
                                             A Member of the Deustche 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.




November 24, 2003                            /s/Richard T. Hale
                                             Richard T. Hale
                                             Chief Executive Officer
                                             Scudder High Income Fund, a
                                             series of Scudder High Income
                                             Series




                                             Deustche Asset Management [LOGO]
                                             A Member of the Deustche 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.




November 24, 2003                             /s/Charles A. Rizzo
                                              Charles A. Rizzo
                                              Chief Financial Officer
                                              Scudder High Income Fund, a
                                              series of Scudder High Income
                                              Series