We consider parametric instabilities of a circularly polarized Alfv¿n wave propagating along the background magnetic field. The perturbations too are assumed to propagate along the background field. The new feature of this work is the presence of a second ion species (He++) which drifts relative to the protons. Even though its abundance is small, the He++ modifies the dispersion relation of the ''pump'' Alfv¿n wave and introduces a new sound wave (alpha sound) in addition to the usual sound wave carried primarily by the electrons and protons. These features modify the wave couplings leading to instability and introduce new wave couplings which lead to several new instabilities which may be of interest in the solar wind. In particular, we will find instabilities which are close to the He++ gyroresonance. This may provide a means of directly transferring Alfv¿n wave energy to the alpha particles, if the alphas are able to resonantly extract energy from the unstable waves, without quenching the instability altogether. We will also find instabilities which are close to the alpha particle sound speed. The alpha particles in this case will tend to absorb energy via Landau damping, and this may again represent a mechanism of transferring Alfv¿n wave energy to the alpha particles, if the Landau damping does not suppress the instability. Finally, we will find new instabilities close to the proton cyclotron resonance, which may serve as a new mechanism for transferring wave energy into the protons. Some similar results have been recently obtained independently by Goldstein (1990). ¿ American Geophysical Union 1993