A collisionless spatially nonuniform plasma is considered in a finite conducting cylinder in a uniform magnetic field. The magnetic field is increased by a small fractional amount over the critical value for onset of instability. A single mode grows and is saturated by nonlinear effects. Analytic expressions are obtained for the time‐asymptotic saturation amplitude and frequency shift. Indeterminate equations and singular functions are resolved by methods similar to those used earlier in the one‐dimensional bump‐on‐tail analysis, and the form of the modified equilibrium distribution and potential is obtained. A specific numerical example demonstrates that saturation is due to increased ion Landau damping, and that this saturated amplitude is unstable to small deviations. Hence, the onset of the instability is predicted to be of the ’’hard’’ variety. This result holds both in the ’’quasi‐linear’’ approximation and in the full nonlinear case.