An analysis of ion cyclotron resonance heating in a plasma containing two ion species is given. Particular emphasis is placed on the important case of comparable concentrations of the two species. The properties of ion-Bernstein waves in such a plasma are discussed. A summary of the cutoff– resonance (Budden) and cutoff–resonance–cutoff (triplet) configurations is given and an analytic expression obtained for the Budden transmission coefficient (relevant also to the triplet case), which is valid for any concentration ratio of the two-ion species. A formula for the damping coefficient of the ion hybrid wave is obtained and a ray tracing code is used to illustrate the absorption of this mode by electrons close to the two-ion hybrid resonance. The reduced, second-order fast wave equation is solved numerically, illustrating the transition from strong electron heating through mode conversion at the two-ion hybrid resonance to direct electron damping of the fast wave in a high beta plasma.