This paper shows how an initially isotropic spherical shell velocity distribution of cometary or interstellar pickup ions can become thermalized. The basic instability mechanism responsible for the thermalization is based on papers by Wu and Yoon (1990) and Yoon (1990). The unstable mode is in the Alfv¿n mode branch and propagates in an oblique direction, with the mode stable for exactly parallel and perpendicular propagations. The present paper discusses the nonlinear evolution of the ion distribution as well as the unstable waves. The method is based on the self-consistent quasi-linear equations. It is found that the thermalization can take place in 6.4¿103 to 1.6¿104 ion gyroperiods for the parameters used in the present analysis, while the unstable waves can grown to an appreciable level of the initial fluctuation. ¿ American Geophysical Union 1992