The space‐time evolution of the drift‐cyclotron instability as influenced by the nonlinear shift in the ion‐cyclotron frequency is studied analytically, numerically, and by computer simulation. The analysis is specialized to the case of a single coherent wave with frequency near both a cyclotron harmonic and the ion diamagnetic frequency. Such an analysis is motivated by observations of large‐amplitude ion‐cyclotron waves in the 2XIIB mirror experiment, which were highly monochromatic and often exhibited these frequency characteristics. A nonlinear dispersion relation describing saturation of the instability is derived by means of a self‐consistent analytical solution of the Vlasov–Poisson equations to third order in the wave amplitude. Solitary wave and self‐similar solutions are obtained that describe nonlinear wave propagation. Numerical solution of a nonlinear evolution equation and particle simulation confirm the analysis.