The spectrum of waves in a two-ion-species plasma at frequencies up to the ion-ion hybrid resonance frequency is investigated. A cylindrical plasma column of uniform density and magnetic field, and surrounded by a vacuum, is firstly analysed, and the results are checked when plasma and magnetic field nonuniformities are allowed for. A new m=-1 mode is found to exist at frequencies just above the ion-ion hybrid resonance frequency. This mode has much in common with a previously reported m=-1 mode above the Alfven resonance frequency in that it can have surface wave properties and its dispersion curve merges into the ion-ion hybrid resonance at a critical value of the axial wavenumber. The mode survives as an ion-ion resonance damped wave in a nonuniform density plasma or magnitude field. The m=+1 wave dispersion relation is found to pass through the ion-ion hybrid resonance via a mode crossing, with connection to a hybrid global eigenmode below the hybrid resonance, and connection to a surface wave above the hybrid resonance.
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