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The frequency multiplication effects in high-power free-electron masers (FEM) with Bragg cavities were studied to provide the advance of the oscillators into short-wavelength bands. Theoretical analysis of frequency-multiplying FEMs was carried out within the framework of the averaged coupled-wave approach. Proof-of-principle experiments were performed based on a moderately relativistic induction linac LIU-3000 (JINR). As a result, an FEM multiplier operated with a megawatt power level in the 6-mm and 4-mm wavelength bands at the second and third harmonics, respectively, was realized. The possibility of using two-mode bichromatic FEMs for powering a double-frequency accelerating structure was discussed

High-power free-electron maser operated in a two-mode frequency-multiplying regime