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                                                              Exhibit 99.906cert

Pursuant to Section 906 of the Sarbanes-Oxley Act of 2002 (subsections (a) and
(b) of section 1350, chapter 63 of title 18, United States Code), each of the
undersigned officers of PIMCO High Income Fund (the "Registrant"), do hereby
certify, to such officer's knowledge, that

     (1)  The Semi-Annual Report on Form N-CSR for the period ended September
          30, 2004 (the "Form N-CSR") fully complies with the requirements of
          Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

     (2)  The information contained in the Form N-CSR fairly presents, in all
          material respects, the financial condition and results of operations
          of the Registrant.

Dated: December 6, 2004

By /s/ Brian S. Shlissel
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Brian S. Shlissel
President and Chief Executive Officer

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A signed original of this written statement required by Section 906, or other
document authenticating, acknowledging, or otherwise adopting the signature that
appears in typed form within the version of this written statement required by
Section 906, has been provided to PIMCO High Income Fund and will be retained by
PIMCO High Income Fund and furnished to the Securities and Exchange Commission
or its staff upon request.

This certification is being furnished solely pursuant to 18 U.S.C. ss 1350 and
is not being filed as part of the Report or as a separate disclosure document.

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Pursuant to Section 906 of the Sarbanes-Oxley Act of 2002 (subsections (a) and
(b) of section 1350, chapter 63 of title 18, United States Code), each of the
undersigned officers of PIMCO High Income Fund (the "Registrant"), do hereby
certify, to such officer's knowledge, that

     (3)  The Semi-Annual Report on Form N-CSR for the period ended September
          30, 2004 (the "Form N-CSR") fully complies with the requirements of
          Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

     (4)  The information contained in the Form N-CSR fairly presents, in all
          material respects, the financial condition and results of operations
          of the Registrant.

Dated: December 6, 2004

By /s/ Lawrence G. Altadonna
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Lawrence G. Altadonna
Treasurer, Principal Financial and Accounting Officer

A signed original of this written statement required by Section 906, or other
document authenticating, acknowledging, or otherwise adopting the signature that
appears in typed form within the version of this written statement required by
Section 906, has been provided to PIMCO High Income Fund and will be retained by
PIMCO High Income Fund and furnished to the Securities and Exchange Commission
or its staff upon request.

This certification is being furnished solely pursuant to 18 U.S.C. ss 1350 and
is not being filed as part of the Report or as a separate disclosure document.