Linear vestibuloocular reflexes (LVORs) stabilize retinal images by producing eye movements to compensate for linear head motion. LVOR response characteristics depend upon gaze relative to the motion axis and binocular fixation distance. LVOR sensitivity during NO-axis motion increases as gaze eccentricity relative to the motion axis increases and as binocular fixation distance decreases. To fixate targets during forward head motion and rightward gaze, eyes must move to the right, but when looking left, the eyes must move to the left. In this study, LVORs were measured (binocular search coils) during 5.0 Hz horizontal motion along axes between and including NO and IA. This reorients head and otolith inputs relative to linear motion. We found that LVORs follow the same kinematics regardless of eye position in the head or head orientation relative to motion. Eye position information must be quickly and accurately integrated with otolith inputs to determine eye position (gaze) relative to linear head motion in space. The LVOR provides a behaviorally useful reflex for maintaining ocular fixation on visual targets during translation along any axis.