A catalytic reactor is considered, consisting of parallel capillaries on which a mixture of reactants flows. The catalyst is put on the internal surface of these capillaries. The possibility of increasing the effectiveness of the considered type of catalytic reactor is shown in the case of realization of the chemical reaction in artificially created non-steady-state conditions with simultaneous management of the distribution of active centres on an internal surface of the capillaries. ©2000 American Institute of Physics.