Abstract <p>Using the path integral formalism, quantum-mechanical tunneling is described by instantons—solutions to the equations of system motion in imaginary time. However, in imaginary time, this formalism is suitable only for studying the characteristics of a system in thermodynamic equilibrium and is not applicable to significantly nonequilibrium phenomena. Therefore, it is necessary to develop an approach that takes into account instanton solutions within the framework of the real-time path integral. This paper takes a step in this direction by generalizing the Gutzwiller trace formula, derived within the real-time formalism, for the density of states of a quantum-mechanical system in a tunnel-type potential. It is shown that to obtain real values of the level splitting in a symmetric double-well potential, it is necessary to take into account approximate solutions to the equations of motion in imaginary time, corresponding to multi-instanton configurations.</p>