Extracellular thermostable alpha -amylase (EC 3.2.1.1) and intercellular a-galactosidase (EC 3.2.1.22) from one fermentation of a thermophilic and aerobic Bacillus sp.JF(2) strain were studied and modelled. The cell growth of the thermophilic Bacillus sp.JF(2) strain could be expressed by the Monod model, the mu (max) was 0.084/h, the activation energy for cell growth and death was E-g=7.42 and E-d=-18.8 cal/g mol K. The thermostable alpha -amylase production was expressed by a model combining growth-associated and non-growth-associated models. Intercellular alpha -galactosidase production was expressed by the growth-associated model; and the relationship equation between the substrate, cell growth, and two enzyme production was also defined, and the all constants were defined. (C) 2001 Elsevier Science Ltd. All rights reserved.