Kinetic aspects of enzymatic reactions proceeding in the autocatalytic mode are considered. Kinetic analysis of a mechanism with proenzyme-enzyme interaction and of mechanism in which activation involves an interaction with the product of enzymatic reaction is presented. It is shown that these mechanisms are distinguished by the dependences of kinetics of the process on enzyme and substrate concentrations. Method is developed for the determination of concentration of active centers of enzyme in the case of activation by reaction product. Conclusions obtained are illustrated using autocatalytic enzymatic systems such as trypsin-trypsinogen and bacterial hydrogenases-hydrogen-4,4'-dimethylbipyridinium.