Item 11(b).

          CERTIFICATION UNDER SECTION 906 OF SARBANES-OXLEY ACT OF 2002

     Name of Issuer:  T. Rowe Price GNMA Fund

     In connection with the Report on Form N-CSR for the above named issuer, the
     undersigned hereby certifies, to the best of his knowledge, that:

     1.  The Report fully complies with the requirements of Section 13(a) or
         15(d) of the Securities Exchange Act of 1934;

     2.  The information contained in the Report fairly presents, in all
         material respects, the financial condition and results of operations of
         the Issuer.





     Date:  July 16, 2004                            /s/ James S. Riepe
                                                     James S. Riepe
                                                     Principal Executive Officer

     Date:  July 16, 2004                            /s/ Joseph A. Carrier
                                                     Joseph A. Carrier
                                                     Principal Financial Officer