Rebound nystagmus, a common cerebellar sign, is a transient nystagmus that appears on returning to straight-ahead gaze after prolonged eccentric gaze. The slow phases of rebound nystagmus are in the direction of prior eccentric gaze. After eccentric gaze, healthy subjects also show rebound nystagmus when fixation is removed. Rebound nystagmus is thought to be related to the function of the oculomotor neural integrator—the circuit that ensures accurate gaze holding after any eye movement—but the exact mechanism of rebound nystagmus is unknown. Here, we combine experimental data with mathematical modeling to test several hypotheses for the generation of rebound nystagmus. We show that two mechanisms contribute, one relies on vision and the other does not. Future experiments must determine if (1) the non-visual mechanism is related to eye position or to eye velocity signals and (2) whether these signals are based on afferent (proprioception) or efferent (corollary) information.