Oscillating an animal out-of-phase simultaneously about the roll and pitch axes ("wobble") changes continuously the orientation of the head relative to gravity. For example, it may gradually change from nose-up, to ear-down, nose-down, ear-down, and back to nose-up. Rotations about the longitudinal axis ("spin") can change the orientation of the head relative to gravity in the same way, provided the axis is tilted from vertical. During both maneuvers, the otolith organs in the inner ear detect the change in head orientation relative to gravity, whereas the semicircular canals will only detect oscillations in velocity (wobble), but not any rotation at constant velocity (spin). Geometrically, the whole motion can be computed based on information about head orientation relative to gravity and the wobble velocity. We subjected monkeys (Macaca mulatta) to combinations of spin and wobble and found that the animals were always able to correctly estimate their spin velocity. Simulations of these results with an optimal Bayesian model of vestibular information processing suggest that the brain integrates gravity and velocity information based on a geometrically coherent three-dimensional representation of head-in-space motion.