In eukaryotes, the 20S proteasome contains two chymotrypsin-like, two trypsin-like, and two active sites shown here to have caspase-like specificity. We report that certain sites allosterically regulate each other's activities. Substrates of a chymotrypsin-like site stimulate dramatically the caspase-like activity and also activate the other chymotrypsin-like site. Moreover, substrates of the caspase-like sites inhibit allosterically the chymotrypsin-like activity (the rate-limiting one in protein breakdown) and thus can reduce the degradation of proteins by 26S proteasomes. These allosteric effects suggest an ordered, cyclical mechanism for protein degradation. We propose that the chymotrypsin-like site initially cleaves ("bites") the polypeptide, thereby stimulating the caspase-like sites. Their activation accelerates further cleavage ("chewing") of the fragments, while the chymotrypsin-like activity is temporarily inhibited. When further caspase-like cleavages are impossible, the chymotryptic site is reactivated and the cycle repeated.