The nonlinear problem of MHD wave excitation in plasma by an ion beam with a ring distribution function was solved. We studied how the steepened wave profiles grew out of low-frequency Alfv¿n fluctuations excited by the ion beam in plasma. Two types of nonlinearities are taken into account: (1) strong nonlinearity of resonant ions (beam ions) due to trapping and bounce-oscillation effects and (2) weak nonlinearity of nonresonant particles (plasma particles) that leads to mode coupling and steepening of the wave profile. The spectral method in concert with a hybrid method of resonant simulation was used in this study. The wave excitation, saturation, and subsequent nonlinear evolution were studied.