The interactions of waves and trapped electrons are described by a closed system of three nonlinear coupled equations. The model has applications to many aspects of wave-particle interactions in the magnetosphere. Nonlinear numerical solutions pertinent to auroral pulsations have been computed for realistic ranges of physical parameters. The results confirm that precipitation pulsations can be initiated by either an injection of energetic trapped particles or an increase in the plasma ionization density. Relaxation of the system results in cyclic phase trajectories about a (quasi equilibrium) point that is not located at the initial equilibrium point. That observation may explain the tendency of auroral pulsations to appear superimposed upon an increase in the general rate of electron precipitation. The results also imply that precipitation pulsations are most readily initiated by an encounter of drifting energetic electrons with a region of enhanced cold plasma density. ¿ American Geophysical Union 1987