In this paper we discuss the role played by a radiofrequency induced electric field on the current drive efficiency of electron cyclotron (EC) waves when there are locked or rotating magnetic islands in the plasma. The problem is addressed by numerical solution of the Fokker–Planck equation within the framework of the quasilinear theory incorporating realistic features of the geometry of the magnetic islands. The modes 2/1 and 3/2 are analysed. Our main result is the reduction, although not the complete suppression, of the level of the current driven by the waves in the short time scale needed for the induced field to diffuse away from the islands region. Another finding is the suppression of quasilinear effects on the EC current drive efficiency in the case of locked islands for both 2/1 and 3/2 modes.