The purpose of this work is to construct an approximate nonlinear theory of a klystron amplifier in which a medium with complex conductivity or with metamaterials with negative permittivity is located between the input and output cavities instead of the drift space. Within the framework of the constructed theory, calculate the output characteristics (gain, output power and efficiency) of the described device and compare the results with the classic two-cavity klystron. Methods. Since the principle of operation of a resistive wall amplifier and an amplifier with complex conductivity is precisely the wave process, to construct a nonlinear theory, the Ovcharov–Solntsev wave method is used, the main idea of which is to consider the variable part of the electron passage angle (periodic function of the time of flight) using a series Fourier with few members. The following model is investigated: an ion-compensated cylindrical electron stream penetrates the input resonator, modulates in speed, and flies into a medium with complex permittivity and/or with arbitrary complex conductivity. The electron beam is described in terms of a one-dimensional model. Penetrating the grids of the output cavity, the electron beam induces a high-frequency field in it. Results and conclusion. It is shown that if instead of the drift space between the input and output resonators there is a medium with complex dielectric constant, then the distance between the resonators can be reduced by more than half with an increase in the output characteristics.