The vestibulo-ocular reflex (VOR) serves to stabilize images on the retina by rotating the eyes in the direction which opposes angular (aVOR) or linear (IVOR) head movement. The aVOR responds to rotations in any plane. Head rotations about the naso-occipital axis (roll) are accompanied by compensatory torsional eye movements, with gains typically less than 0.7. However, geometric considerations suggest that the response should not be restricted to torsion, and that horizontal, vertical, and torsional response components should depend upon eye position relative to the axis of rotation. Since eye position can differ for the two eyes (e.g., during convergence), the response to head roll should be accordingly disconjugate. Further, because the eyes are typically displaced from the axis of rotation, head roll entails a calculable translation of the eyes in space, and compensation for this component of motion is expected to add to the response to angular motion. The translational response component should be modulated by fixation distance. To test these geometric considerations in the aVOR, we investigated the three-dimensional ocular responses of squirrel monkeys to head roll. Torsional aVOR responses were accompanied by vertical components which were modulated by horizontal gaze position, and by horizontal components which were modified by vertical gaze position. The vertical response components were often appropriately disconjugate, and even opposing, yielding responses that appeared "see-saw" in character.(ABSTRACT TRUNCATED AT 250 WORDS)