The theory of multiple inhibition kinetics has been extended to enzymes for which one inhibitor is noncompetitive and the other exhibits mixed inhibition. Plots of reciprocal velocity versus the concentration of either inhibitor at various fixed concentrations of the second inhibitor are predicted to give parallel lines if binding of the inhibitors is mutually exclusive and intersecting lines if the inhibitors interact at different sites on the enzyme. Application of this analysis to the purple acid phosphatase from bovine spleen in the presence of molybdate (a noncompetitive inhibitor) and phosphate (which exhibits mixed inhibition) results in parallel lines in the reciprocal velocity plots, indicating that phosphate and molybdate compete for a common site; since molybdate is a noncompetitive inhibitor, this site is inferred to be distinct from the site at which substrate binds and is hydrolyzed. Extension of these ideas suggests that phosphate ester substrates should be capable of binding to the molybdate-binding site as well as to the active site, and evidence for substrate inhibition at high substrate concentrations has been obtained. The implications of these findings for interpretation of previous spectroscopic studies of purple acid phosphatase complexes with tetrahedral oxyanions are discussed.