N-CSR Item 10 - Exhibits: Certifications EX-99.906CERT

                          SECTION 906 CERTIFICATION

Pursuant to 18 U.S.C.ss. 1350, the undersigned officers of Federated Government
Income Securities, Inc. (the "Registrant"), hereby certify, to the best of
our knowledge, that the Registrant's Report on Form N-CSR for the period
ended 8/31/03 (the "Report") fully complies with the requirements of Section
13(a) or 15(d), as applicable, of the Securities and 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 Registrant.


Dated: October 23, 2003

/s/ J. Christopher Donahue

Title: President, Principal Executive Officer



Dated: October 23, 2003

/s/ Richard J. Thomas

Title: Treasurer, Principal Financial Officer

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.