The interaction of magnetized, relativistic test particles with a monochromatic electromagnetic wave is analyzed, taking into account the passage through cyclotron resonance in the spatially varying background magnetic field in slab geometry. A resonance-averaged Hamiltonian is used to delineate two distinct regimes. In both cases, termed adiabatic and nonadiabatic, the first adiabatic invariant of the particle is broken during a resonant interaction, leading to change in energy and pitch angle. The adiabatic case is characterized by a limited range of resonant phase and a well-defined value of the change of the invariant. In the nonadiabatic case the phase at resonance ranges over 0 to 2&pgr;, and only the magnitude of the change of the invariant is determined; a phase factor gives the invariant change an effectively random sign. The appropriate regime is determined by a ratio of timescales which, in turn, depends on the particle and wave properties: adiabaticity is favored by large wave amplitudes and small parallel gradients of the geomagnetic field B0. The long-term consequences of the two regimes are explored with a Monte Carlo simulation in the form of an iterated mapping. In a particular example, while some particles pitch angle scatter into the loss cone, energy is also removed from the distribution by particles in the adiabatic regime decaying in energy owing to repeated resonant interactions with the wave. Important potential magnetospheric applications include flux levels in the inner radiation belts, observations of pancake pitch angle distributions, and energization of storm time killer electrons. ¿ 2000 American Geophysical Union