Recently, Gomberoff and Elgueta (1991) showed that in a plasma composed of anisotropic protons and alpha particles drifting along an external magnetic field with a small velocity relative to the protons, strong left-hand polarized electromagnetic ion cyclotron waves can be generated. These waves can accelerate the alpha particles to velocities well in excess of the proton bulk velocity. Here we assume a more realistic model of the solar wind by considering a double-humped proton distribution. It is shown that the secondary proton beam has no important effects on the ion cyclotron waves for beam densities of the order of those observed in fast solar wind conditions. The fact that the alpha proton drift velocity is modulated by the Alfv¿n velocity remains unexplained. ¿ American Geophysical Union 1992