When particle orbits are trapped very near a cyclotron harmonic resonance, the quasilinear concept of weakly perturbed, uncorrelated passages through resonance breaks down, and nonlinear effects become important. In numerical as well as analytic studies, it is demonstrated that relativistic detuning of the resonance can be important for electrons even at low initial energies (∼20 eV) and that coupling to perturbed parallel motion can lead to strong interactions for values of the turning point where the wave frequency differs from a harmonic multiple of the bounce‐averaged gyrofrequency by an integral multiple of the bounce frequency. The resultant motion is described by large periodic energy excursions for which small‐angle Coulomb collisions or other randomization processes are required to realize net heating. Analytic formulas are derived describing the energy excursion behavior and heating in a mildly relativistic limit. Also, a Monte Carlo numerical model of the collisional effects on the orbits has been employed to study electron heating at the second‐harmonic cyclotron resonance and to test the analytic results. In certain regimes of collisionality, a strong enhancement over quasilinear heating has been found.