He won re-election in 1998 with 74% of the vote, which was the largest margin of victory by any governor up for election in 1998, and one of the largest margins of victory in Kansas gubernatorial history. Graves was barred from running for a third term as governor by Kansas state law, and was succeeded by DemocratKathleen Sebelius in January 2003. Serving with him as lieutenant governor were Sheila Frahm (1995–1996), whom he appointed to fill Bob Dole's seat in the Senate, and Gary Sherrer (1996–2003).