The ponderomotive force exerted by a standing electromagnetic wave in an infinite, magnetized plasma containing two ion species is examined. A perturbation analysis is developed to solve the nonlinear wave equation subject to the constraint that the total number of particles of each species is conserved. Detailed calculations are presented for an ion cyclotron wave, for which large modifications of the ion densities result from the influence of the ponderomotive force. To determine the range of validity of the perturbation analysis, the results are compared with those obtained by numerical integration of the nonlinear wave equation.