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The possibilities and conditions of effective interaction, in particular acceleration, of charged particles by the field of an intense plane electromagnetic wave in the presence of an external constant magnetic field are considered. It is shown that the well-known conditions of cyclotron resonances require generalization. New conditions for the resonant interaction of charged particles are formulated, which contain not only the strength of the external magnetic field (as the well-known conditions of cyclotron resonances) but also the field strength of the wave. Cases of both small wave field strengths, so large, are considered. It is shown that new resonance conditions open up new possibilities for effective particle acceleration.