Current drive by electron cyclotron waves in toroidal geometry is investigated by means of a bounce‐averaged Fokker–Planck code. The case of the extraordinary mode at a frequency lower than the electron gyrofrequency is studied in detail for a wave packet of finite width, carrying a power in the megawatt range, which is absorbed away from the plasma center. It is shown that in this case, because of the interplay of quasilinear and trapping effects (i) the current drive efficiency is strongly power dependent and (ii) wave absorption at the inboard part of the magnetic surfaces does not maximize the efficiency, in contrast to the results of linear theory.