Generation of ELF and VLF waves in the HF heater modulated polar electrojet is numerically studied. Illuminated by an amplitude modulated HF heater, the electron temperature of the electrojet is modulated accordingly. This, in turn, causes the modulation of the conductivity and thus the current of the electrojet. Emissions are then produced at the modulation frequency and its harmonics. The present work extends the previous one on a thermal instability to its nonlinear saturation regime. Two heater modulation schemes are considered. One modulates the heater by a rectangular periodic pulse. The other one uses two overlapping heater waves (beat wave scheme) having a frequency difference equal to the desired modulation frequency. It is essentially equivalent to a sinusoidal amplitude modulation. The nonlinear evolutions of the generated ELF and VLF waves are determined numerically. Their spectra are also evaluated. The results show that the signal quality of the second (beat wave) scheme is better. The field intensity of the emission at the fundamental modulation frequency is found to increase with the modulation frequency, consistent with the Tromso observations. ¿ 1998 American Geophysical Union