Abstract The aggregation of κ-casein on incubation with the rennin-like acid protease from Mucor pusillus has been studied by stopped-flow spectroscopy. Kinetic equations have been derived describing the aggregation in terms of the lag period, τ, prior to aggregation and the maximum rate of change in absorption during aggregation, V. A considerable substrate inhibition was found with the concentration of κ-casein used (0.05–1.0 mg/ml). From measurements of τ, the substrate inhibition constant was found to be 0.6 mg/ml. The K m for κ-casein has been estimated from inhibition experiments with Ca 2+ to be 0.01–0.02 mg/ml. While Ca 2+ is necessary for the clotting of milk, Ca 2+ was found to inhibit the aggregation of κ-casein. The decrease in 1/τ was competitive with regard to the concentration of κ-casein, while the decrease in V was competitive with regard to the enzyme concentration. The present results suggest that the high specificity of the enzyme in the clotting of milk may partly be accounted for by the very low value of K m involved in the aggregation of κ-casein.