Simple models are described which investigate the combined effects on solar wind He++of resonant and nonresonant acceleration by left‐hand transverse waves. The principal points are the following. (1) For a wide range of parameters, (υα– υp) at 1 AU is close to the effective phase speed of the left‐hand waves. (2) The most important factor in determining υα/υpat 1 AU is whether the high‐frequency left‐hand waves are predominantly outward propagating, inward propagating, or a mix of both. The resonant acceleration may be more important than the effects of heating or stream‐stream interactions. (3) Reasonable values of υα/υpat the sun (and ofnα/npat 1 AU) are obtained for a power law index α ≅ 1.5 in the wave power spectrum if the effective phase speed of the resonant waves near the sun is not small in comparison to the Alfvén speed there. This requires a substantial level of high‐frequency power in outward going waves at the sun, which cannot come from heat‐conduction‐driven instabilities. (4) The present models do not allow one to decide whether the coronal He++abundance is greater or less than that at 1 AU. (5) Some of the models show a positive correlation betweennα/npand υpat 1 AU, roughly as has been observed. (6) The models suggest that variations innα/npat 1 AU can result from variations in the wave properties near the sun and not necessarily from variations in the coronal abundance. (7) Some models indicate that (υα/υp) may decrease with increasing r in the vicinity of 1 AU. (8) The resonant acceleration is more efficient than Coulomb friction in the sense that it does not exhibit a runaway effect. (9) Observations of minor species may be used to deduce wave properties a