1. The vestibuloocular reflex (VOR) was examined in four alert monkeys during rotations of the head about torsional, vertical, horizontal, and intermediate axes. Eye positions and axes were recorded in three dimensions (3-D). Visual targets were used to optimize gaze stabilization. 2. Axes of eye rotation during slow phases showed small but systematic deviations from collinearity with the axes of head rotation. These noncollinearities apparently resulted from vector summation of torsional, vertical, and horizontal VOR components with different gains. 3. VOR gain was lowest about a head-fixed torsional axis that was correlated with the primary gaze direction, as determined by Listing's law for saccades. As a result, rotation of the head about a partially torsional axis produced noncollinear slow phases, with axes that tilted toward Listing's plane. 4. During slow phases, eye position changed not only in the direction of rotation, but also systematically in other directions. Even axes of eye rotation within Listing's plane caused eye position to move out of the plane to a torsional position that was then held. Thus Listing's law for saccades cannot be a product of plant mechanics. 5. VOR slow phases were simulated with the use of a model that incorporated 3-D rotational kinematics into the indirect path and the oculomotor plant. This demonstrated that the observed pattern of position changes is the expected consequence of rotating the eye about a fixed axis and that to hold these positions the indirect path must employ a 3-D velocity-to-position transformation. 6. Quick phases not only corrected the violations of Listing's law produced by slow phases but anticipated them by directing the eye toward a plane rotated in the direction of head rotation. This was modeled by inputting the vestibular signal to a Listing's law operator that is shared by the quick phase and saccadic systems.