We investigate by computer simulation experiments the nonlinear behavior of mixed H+-He++ plasma systems under the particular physical conditions found by the linear theory to allow the parallel propagation of only weakly damped electromagnetic ion cyclotron waves at the alpha particle cyclotron frequency. Here the waves are generated by anisotropic proton populations. The essentially nonlinear results of our computer simulations indicate a strong damping of the parallel propagating electromagnetic ion cyclotron waves and a significant dip in the energy spectrum, both centered cyclotron waves and a significant dip in the energy spectrum, both centered at about &ohgr;=&OHgr;&agr;. ¿ American Geophysical Union 1988