The effects of a heavy minority on Alfve´n wave heating are examined in a linearized circular cylindrical tokamak model. It is shown that a suitable minority concentration and radially varying charge profile produces a two‐ion hybrid resonance in the plasma interior and an Alfve´n wave resonance near the edge. The latter situation, which gives rise to cold plasma surface Alfve´n eigenmodes (SAE’s), was described in Part I [Phys. Fluids B1, 2353 (1989)] for a pure plasma. Here, numerical results, exhibiting substantial absorption in the hybrid layer as a result of the dissipation of these modes, are presented. It is shown that the poloidal mode number strongly affects the amount of the energy absorbed in the hybrid layer. Generally, electron heating due to electron Landau and collisional damping of SAE’s and two‐ion hybrid fields [&ohgr;>(&ohgr;c2)max, with &ohgr;c2being the fundamental minority gyrofrequency] dominates minority heating excepting for cases whenk∥, the parallel wavenumber, is large enough that no SAE occurs near the plasma edge. For the largerk∥system, there occurs a stronger coupling between the two‐ion hybrid and fundamental minority gyroresonance layers, resulting in comparable electron and minority heating. The majority heating is zero everywhere because &ohgr;<(&ohgr;c1)min, where &ohgr;c1is the fundamental majority gyrofrequency.