The kinetic model of the hydrolysis of lactose with a P-galactosidase from Kluyveromyces fragilis immobilized on a commercial silica-alumina (KA-3, from Sudchemie) has been determined. A wide experimental range of the main variables has been employed: temperature, concentrations of substrate, and products and concentration of enzyme. The runs were performed in a complex buffer with the salt composition of milk. The effect of pH and temperature on the stability and the activity of the enzyme have been studied. The optimum pH for the enzyme activity was, approximately, seven. The immobilized enzyme was more stable than the free one at acidic pH, but more instable at basic pH. The maximum temperature used for the hydrolysis runs performed to select the kinetic model was 40 degrees C, so inactivation of the enzyme during the kinetic runs has been avoided. Agitation, concentration of enzyme in the solid and particle size were selected to ensure that the overall rate was that of the chemical reaction. Eleven kinetic models were proposed to fit experimental data, from first order to more complex ones, such as those taking into account inhibition by one of the compounds involved in the hydrolysis reaction. Applying statistical and physical criteria, a Michaelis-Menten model with a competitive inhibition by galactose has been selected. The model is able to fit the experimental data correctly in the wide experimental range studied. Finally, the model obtained is compared to the one selected in a previous work for the hydrolysis of lactose with the free enzyme.