It has been established in recent years based on theoretical discussions and observations that the solar wind can pick up newborn cometary ions, and the pickup ions usually form a shell distribution. A relevant question is what can subsequently happen to such a distribution. To address this problem, two publications have discussed the linear stability of the shell distribution [Freund and Wu, 1988; Gary and Sinha, 1989>. In the present discussion, both the linear and nonlinear development of the waves and the evolution of the initial shell distribution are investigated by numerical simulations. For this purpose, the linear theory is also generalized so that some additional important effects are incorporated. ¿ American Geophysical Union 1989