Stage-specific proteolysis of mitotic cyclins is fundamental to eukaryotic cell cycle regulation. We found that yeast Hct1, a conserved protein of eukaryotes, is a necessary and rate-limiting component of this proteolysis pathway. In hct1 mutants, the mitotic cyclin Clb2 is highly stabilized and inappropriately induces DNA replication, while G1 cyclins and other proteolytic substrates remain short-lived. Viability of hct1 mutants depends on SIC1. This and further results suggest that inhibition of cyclin-dependent kinases may compensate for defects in cyclin proteolysis. Remarkably, elevated levels of Hct1 ectopically activate destruction box– and Cdc23-dependent degradation of Clb2 and cause phenotypic effects characteristic for a depletion of M-phase cyclins. Hct1 and the related Cdc20 may function as substrate-specific regulators of proteolysis during mitosis.