Аннотация:Tunnel dynamics described by the one-dimensional nonstationary Schrödinger equation with a potential periodically depending on time was studied numerically and analytically. Quasi-energy levels were found in the second order with respect to perturbation parameter powers. The dependence of the rate of tunneling on potential parameters was found numerically, and the results were analyzed using the two-level model. The condition of tunneling "quenching" for an arbitrary initial state was obtained.