The electron motion at cyclotron resonance in the presence of a homogeneous time dependent magnetic field and a standing h.f. electric field is studied in the relativistic approximation. It is shown that the relativistic mass of the electron "follows" an increasing magnetic field in such a way that the ECR condition is fulfilled during a long time, independently of the initial phase and velocity, if the growth of the magnetic field is not too sharp. The results of the approximate theory are confirmed by numerical computations from the exact relativistic equation of motion. Possibilities of using this effect for ion accelerating up to 10 MeV energy range, producing powerful pulses of γ-ray bremstrahlung and strong synchroton emission sources are indicated. © 1980 IOP Publishing Ltd.