Experiments demonstrate that electrical stimulation of the auditory nerve evokes qualitatively different responses to those of normal hearing. We apply a self-exciting point process model to explain and predict both responses. For acoustic stimulation, the model predicts the shape of the per- stimulus time histogram (PSTH), the average firing rate, and the maximum possible firing rate. The model also predicts the PSTH for pulsatile electric stimulation. The model is used to parametrize the response differences between electric and acoustic neural stimulation, and to design electrical stimuli which cause single auditory neurons to respond similarly to the normal hearing situation. Such stimuli should find application in advanced cochlear implants.