The proteolytic activity of the eukaryotic 20S proteasome is stimulated by a multisubunit activator, PA700, which forms both 1:1 and 2:1 complexes with the proteasome. Formation of the complexes is enhanced by an additional protein assembly called modulator, which also stimulates the enzymatic activity of the proteasome only in the presence of PA700. Here we show that the binding of PA700 to the proteasome is cooperative, as is the activation of the proteasome's intrinsic peptidase activity. Modulator increases the extent of complex formation and peptidase activation, while preserving the cooperative kinetics. Furthermore, the increase in activity is not linear with the number of PA700 assemblies bound to the proteasome, but rather with the number of proteasome-PA700 complexes, regardless of the PA700:proteasome stoichiometry. Hence the stimulation of peptidase activity is fully (or almost fully) effected by the binding of a single PA700 to the 20S proteasome. The stimulation of peptidase by modulator is explained entirely by the increased number of proteasome-PA700 complexes formed in its presence, rather than by any substantial direct stimulation of catalysis. These observations are consistent with a model in which PA700, either alone or assisted by modulator, promotes conformational changes in the proteasome that activate the catalytic sites and/or facilitate access of peptide substrates to these sites.