beta-Cyclodextrin changes the kinetic peculiarities of microbial 1-en-dehydrogenation of 6 alpha-methylhydrocortisone : the reaction rate, degree of conversion and respiratory-chain activity are increased. Respiratory-chain activity in the presence of beta-cyclodextrin is increased both in the presence and in the absence of 6 alpha-methylhydrocortisone. A mathematical model is proposed to describe the kinetics of the process. This model suggests the formation of different multi-component complexes consisting of inclusion complexes and the functional unit involving the enzyme and the respiratory chain. All the parameters of the model were estimated by data fitting. In the model framework the formation of multi-component complexes leads to an increase of the maximal reaction rate and to a decrease of substrate inhibition. An approach is suggested for optimisation of 6 alpha-methylhydrocortisone 1-en-dehydrogenation in the presence of beta-cyclodextrin. The optimal concentrations of 6 alpha-methylhydrocortisone and beta-cyclodextrin have been calculated.