The sequential hydrolysis of cheese whey proteins can improve physical, chemical and organoleptic properties of this dairy by-product, increasing its applications in the food and pharmaceutical industry. The hydrolysis of polypeptides (50degreesC, pH 9.5), catalyzed by Alcalase((R)) immobilized on 10% agarose (weight basis), activated with linear aliphatic aldehyde groups (glyoxyl-agarose), is studied here. The reaction substrate (polypeptides) is the product of a previous, sequential hydrolyses of cheese whey proteins by trypsin, chymotrypsin and carboxypeptidase A. A Michaelis-Menten model with product inhibition was fitted to the experimental data after long-term batch assays. Kinetic parameters k. K-M, and K-I Were Correlated with respect to the degree of hydrolysis of the substrate in the upstream proteolyses, thus providing a general, semi-empirical rate equation. With this approach, the kinetic model may be included in process optimization algorithms, which may span different regions of operation for the proteolytic reactors. Parameters k, K-M and K-I ranged from 0.005 to 0.029 mmol/min/U-BAEE, from 4.0 to 13.7 mM. and from 0.19 to 1.56 mM. respectively, when the previous degree of proteolysis (pre-hydrolysis) changed from 20 to 2%. (C) 2004 Elsevier Inc. All rights reserved.