Previous treatments of the excitation of Alfv¿n waves by drift-bounce resonance have been dominated by the linear approximation. We present a nonlinear treatment of the excitation of giant pulsations (Pgs) by drift-bounce resonance and show that nonlinear behavior becomes important well within the typical lifetimes of Pg wave packets. In particular, we show that the nonlinear phase mixing of the resonant particles trapped in the wave fields is of great importance for Pgs, and hence these nonlinearities must be included in calculations of the growth rates of Pgs. We believe that Pg behavior can be described by monochromatic modes exhibiting strong nonlinear wave-particle interactions during injections of resonant particles into the magnetosphere and that the observed growth and damping of Pg wave packets may provide an indication of the temporal variations in the driving resonant particle source population. ¿ 2000 American Geophysical Union