We investigate the preferential acceleration and heating of solar wind alpha particles by the resonant cyclotron interaction with parallel-propagating left-hand-polarized ion cyclotron waves. The Alfv¿n wave spectrum equation is generalized to multi-ion plasmas and a Kolmogorov type of cascade effect is introduced to transfer energy from the low-frequency Alfv¿n waves to the high-frequency ion cyclotron waves, which are assumed to be entirely dissipated by the wave-particle interaction. In order to distribute the dissipated wave energy among the alphas and protons, the quasi-linear theory of the wave-particle interaction is used along with the cold plasma dispersion relation, and a power law spectrum of the ion cyclotron waves is assumed, with the spectral index as a free parameter of the model. The set of three-fluid solar wind equations and the Alfv¿n wave spectrum equation are then solved in order to find fast solar wind solutions. It is found that the effect of the alpha particles on the dispersion relation, omitted in most previous wave-driven solar wind models, has a significant influence on the preferential acceleration and heating of the alphas, especially in the region close to the Sun. With this effect included, the alpha particles can be accelerated to a bulk flow speed faster than the protons by a few hundred kilometers per second and heated by the resonant cyclotron interaction to more than mass-proportional temperature values at several solar radii. However, this mechanism does not yield a differential speed of the order of an Alfv¿n speed and a mass-proportional temperature for the alphas beyond 0.3 AU, as observed, which confirms the same conclusion reached previously by Isenberg and Hollweg [1983> for nondispersive ion cyclotron waves. ¿ 1999 American Geophysical Union