To optimize visual fixation on near targets against translational disturbances, the eyes must move in compliance with geometrical constraints that are related to the distance as well as the speed and direction relative to the target. It is often assumed that the oculomotor system uses the vestibular signals during such movements mainly to stabilize the foveal image irrespective of the peripheral vision. To test this hypothesis, trained rhesus monkeys were asked to maintain fixation on isovergence targets at different horizontal eccentricities during 10 Hz oscillations along different horizontal directions. We found that the two eyes moved in compliance with the geometrical constraints of the gaze-stabilization hypothesis, although response gains were generally small ( approximately 0.5). The best agreement with the gaze stabilization hypothesis occurred for heading directions within +/-30 degrees from straight-ahead, whereas lateral movements exhibited greater variability and larger directional errors that reflected the statistical response variability inherent in the non-linear dependence on heading direction. In contrast to undercompensatory version (conjugate) components, the disjunctive part of the response (vergence) exhibited unity or higher than unity gains. The high vergence gains might reflect a strategy that aims at maintaining the binocular coordination of the gaze lines despite the low gain of the version movements.