The possibility of solving problems of chemical kinetics using artificial neural networks is investigated. The main laboriousness of solving problems of chemical kinetics lies in solving a rigid system of balance equations, whose right side contains the component mass production intensity. This problem can be singled out as a separate stage of solving a system of ordinary differential equations within a common time step of the global problem, and this stage is considered in this paper. A fairly simple model is developed that can solve this problem, which makes it possible to achieve a threefold acceleration of calculations as compared to numerical methods. The resulting neural network operates in a recurrent mode and can predict the behavior of a chemical multicomponent dynamic system many steps ahead.