[en] The necessity to create the RF sources operating in the multifrequency mode is supported by the proposals concerning the suppression of the emittance growth generated inside the RF gun and the possibility to increase the limited accelerated charge by involving into the interaction with the beam, in addition to the fundamental harmonic, the highest harmonics of a RF field with the power ratio up to 10: 1 and the absolute synchronism of changing phase and amplitude ratios of signals. In this paper we present the preliminary results on studying the possibilities of multiple-frequency RF power generation by a single klystron through installation of supplementary high harmonic cavities to the exit one after the main output cavity along the beam direction. The physical motivation of the proposal consists in the effect of lengthy bunch rearrangement due to the interaction with the high-strength decelerating RF fields. The previous experimental data, the 2.5D Particle-In-Cell ARSENAL-MSU code concise description and computer simulation results are given