The relativistic electron nonlinear orbit is investigated for a combined electrostatic plasma wave wiggler and an axial guide magnetic field free electron laser near magnetoresonance. Through simplification, the perpendicular orbit equation is reduced to be identical to the wave‐driven nonlinear oscillator equation [R. C. Davidson, Phys. Lett. A126, 21 (1987)] but with different expressions of parameters. It is found that the maximum perpendicular orbit excursion &Dgr;xmaxis in proportion to (aw/&ggr;0)1/3, which is largely determined by the nonlinear effect, whereawis the wiggler strength and &ggr;0is the initial relativistic factor. The analytical results are in good agreement with the numerical calculation for small ratio ofawto &ggr;0.