[en] Collinear quantum mechanical calculations are reported for the inelastic scattering of He by H⁺₂ below the reaction threshold. The inelastic transition probability curves show a severe oscillatory behavior similar to that recently observed in reaction probability curves for this same system. Perturbation calculations and considerations of the channel phase shifts indicate that the resonance structure is caused by the existence of quasibound (resonance) states of HeH⁺₂. A simple picture is presented which accounts for these quasibound states