Humans routinely use coordinated eye-head gaze saccades to rapidly and accurately redirect the line of sight (Land MF. Vis Neurosci 26: 51–62, 2009). With a fixed body, the gaze control system combines visual, vestibular, and neck proprioceptive sensory information and coordinates two moving platforms, the eyes and head. Classic engineering tools have investigated the structure of motor systems by testing their ability to compensate for perturbations. When a reaching movement of the hand is subjected to an unexpected force field of random direction and strength, the trajectory is deviated and its final position is inaccurate. Here, we found that the gaze control system behaves differently. We perturbed horizontal gaze shifts with long-duration torques applied to the head that unpredictably either assisted or opposed head motion and very significantly altered the intended head trajectory. We found, as others have with brief head perturbations, that gaze accuracy was preserved. Unexpectedly, we found also that the eye compensated well—with saccadic and rollback movements—for long-duration head perturbations such that resulting gaze trajectories remained close to that when the head was not perturbed. However, the ocular compensation was best when torques assisted, compared with opposed, head motion. If the vestibuloocular reflex (VOR) is suppressed during gaze shifts, as currently thought, what caused invariant gaze trajectories and accuracy, early eye-direction reversals, and asymmetric compensations? We propose three mechanisms: a gaze feedback loop that generates a gaze-position error signal; a vestibular-to-oculomotor signal that dissociates self-generated from passively imposed head motion; and a saturation element that limits orbital eye excursion.