The damping of transverse waves, propagating parallel to an external magnetic field, through a low‐density plasma is studied. It is found that there is a limitation on the total amount of energy which may be absorbed in a unit volume of the gas. This saturation phenomenon is predicted on the basis of a particular nonlinear relativistic effect. The total amount of energy absorbed is found to be proportional to the two‐thirds power of the incident radiation energy flux for a low flux, and proportional to the one‐third power for a high flux.