Resonant interaction of an electron beam with a relativistically strong electromagnetic wave of right‐hand circular polarization propagating collinearly along a dc magnetic fieldB0has been studied analytically. The analysis has taken the full nonlinearity of the relativistic effect into account. The result of the relativistic effect on the resonant interaction is to cause the wave intensity to oscillate at a frequency near (&OHgr;0/2&ohgr;)1/2&ohgr;p/&ggr;0. It is found that there is an upper bound on the transverse velocity of the electron achievable through the interaction.