Nonlinear damping of electromagnetic waves propagating along a uniform magnetic field has been calculated by computing nonlinear trajectories for trapped and resonant untrapped particles while using linear theory to describe the rest. This procedure parallels O'Neil's calculation for electrostatic modes, and the results are qualitatively similar. After an initial linear damping, amplitude oscillations set in and the amplitude quickly approaches a finite constant value. The frequency of the amplitude oscillations is temperature dependent. Phase mixing results from the spread in both parallel and perpendicular velocities, giving rise to a more rapid approach to the asymptotic amplitude than for electrostatic modes.