Ion acceleration via wave–particle interaction is experimentally studied in a pulsed ion‐beam–plasma system including nonlinear waves of two different modes. Wave fronts of the two modes are observed to accelerate separately a portion of the upstream plasma ions. To interpret the observed maximum energy of the accelerated ions, it is found that the Boltzmann relation for electrons is not valid for large amplitude waves (&dgr;N/N≳0.3) and it should be replaced by the equation given by Forslund and Shonk [Phys. Rev. Lett.25, 1699 (1970)].