The heating of solar wind alpha particles in hot diamagnetic cavities (HDCs) is examined both through data analysis and computer simulation. The Lockheed Plasma Composition Experiment on ISEE 1 shows more than an order of magnitude increase in the alpha temperature between the solar wind and the HDCs, analogous to the strong solar wind proton heating evidenced in the same transition. A one-dimensional electromagnetic hybrid computer simulation is used to study alpha heating by ion/ion instabilities, where the initial condition is a cool field-aligned proton beam streaming relative to the solar wind protons and alpha particles. Low beam densities excite the proton/proton right-hand resonant instability which pitch angles scatters the beam without significantly heating the alphas. At larger beam densities, the proton/proton nonresonant instability saturates by strong trapping of all three ion components; after saturation the large amplitude magnetic fluctuations lead to stochastic scattering and heating of the ions such that the final temperatures of the alphas are typically greater than the final proton temperatures. These results provide further support to the hypothesis of Thomsen et al. (1988) that the nonresonant instability is the primary source of ion heating in hot diamagnetic cavities. ¿ American Geophysical Union 1990