A general class of solutions is obtained for fully ionized plasmas which admit transverse electromagnetic waves with constant phase velocity. The solutions self‐consistently satisfy Maxwell's equations and Vlasov's equations for both ions and electrons. It is shown, for plasmas admitting such waves, that the mean velocity in the direction of the propagating wave is equal to the wave speed when the plasma is in a stationary state and is different from the wave speed for nonstationary states. A specific set of ion and electron distribution functions is presented which admit monochromatic waves. The associated moments and compatibility relations are calculated.