In the generalized Rutherford equation describing the nonlinear evolution of the width of the magnetic island associated with a neoclassical tearing mode, the effect of localized current drive is represented by a term ¿CD'. We investigate oscillations in ¿CD' originating from the rotation of the island through the electron cyclotron power deposition region and their dependence on the collisional time scale on which the driven current is generated, the rotation period, the island size, and the power deposition width. Furthermore, their consequences for the island growth or the stabilization are analyzed. This work shows that the net result of the oscillations in ¿CD' is a slight increase in the stabilizing effect of electron cyclotron curren...