In many cyclotron resonance masers a beam of gyrating electrons excites standing waves in resonators. Such waves can be represented as a superposition of forward and backward waves that have opposite Doppler shifts of the operating frequency in the reference frame moving with electrons. Correspondingly, for certain axial wave numbers both forward and backward waves can be in cyclotron resonance with gyrating electrons but at different cyclotron harmonics. The theory describing the interaction between electrons and the resonator field in the case of such a double resonance is developed. It is shown that this double resonance can be beneficial when the device operates at symmetric modes while in the case of operation at nonsymmetric modes it always lowers the efficiency. [References: 25]
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