In the present paper, we investigate the trapping of relativistic electrons by intense whistler-modewaves or electromagnetic ion cyclotron waves in the Earth’s radiation belts. We consider thenon-resonant impact of additional, lower amplitude magnetic field fluctuations on the stability ofelectron trapping. We show that such additional non-resonant fluctuations can break the adiabaticinvariant corresponding to trapped electron oscillations in the effective wave potential. Thisdestruction results in a diffusive escape of electrons from the trapped regime of motion and thuscan lead to a significant reduction of the efficiency of electron acceleration. We demonstrate thatwhen energetic electrons are trapped by intense parallel or very oblique whistler-mode waves,non-resonant magnetic field fluctuations in the whistler-mode frequency range with moderateamplitudes around 3 15 pT (much less intense than the primary waves) can totally disrupt thetrapped motion. However, the trapping of relativistic electrons by electromagnetic ion cyclotronwaves is noticeably more stable. We also discuss how the proposed approach can be used toestimate the effects of wave amplitude modulations on the motion of trapped particles.