Nonlinear periodic drift waves are investigated on the basis of a simple perturbation scheme for both the amplitude and inverse frequency. The coefficients for the generation of the forced harmonics are derived, a nonlinear dispersion relation is suggested and a criterion for the onset of the modulational instability is obtained. The results are compared with those obtained with the help of a standard KBM treatment. Moreover, cnoqidal drift waves are suggested and compared to an experimental observation.