We present a continuity equation for the gravitational energy-momentum, which is obtained in the framework of the teleparallel equivalent of general relativity. From this equation it follows a general definition for the gravitational energy-momentum flux. This definition is investigated in the context of plane waves and of cylindrical Einstein-Rosen waves. We obtain the well-known value for the energy flux of plane gravitational waves, and conclude that the latter exhibit features similar to plane electromagnetic waves.