It is shown that radiation friction during charge motion in a plane monochromatic wave results in swinging of the oscillations in a plane perpendicular to the wave propagation direction. An expression is obtained for the characteristic time of motion variation because of radiation losses. It is shown that if the invariant wave intensity parameter is ξ ≫137, radiation friction in the classical domain can influence the motion substantially for a wave phase change Δϕ⪝2π.