1. Horizontal, vertical, and torsional eye movements were recorded (search coil technique) from five squirrel monkeys during horizontal linear oscillations at 0.5, 1.5, and 5.0 Hz, 0.36 g peak acceleration. Monkeys were positioned to produce linear motion in their nasooccipital (NO), interaural (IA), and dorsoventral (DV) axes. Responses of the linear vestibuloocular reflex (LVOR) were recorded in darkness and in the light with the subjects viewing a head-fixed field 22 or 9.2 cm from the eye. The latter condition provided a measure of "visual suppression" of the LVOR (VSLVOR). Responses were also recorded while monkeys viewed earth-fixed targets, which allowed visual enhancement of the LVOR (VLVOR). Vergence angle was recorded in two monkeys to assess directly the point of binocular fixation in space during linear motion. 2. Two LVOR response types, vertical responses during 0.5-Hz NO-axis translation (NO-vertical) and torsional responses at all frequencies during IA-axis oscillation (IA-torsional) could not be compensatory reflexes for head translation because they either move the eye off target (NO-vertical) or tort the eye relative to the visual world (IA-torsional), thereby degrading visual image stability. 3. Other response types are considered compensatory because they help maintain ocular fixation in space during linear head translation. These include horizontal responses to IA-axis motion (IA-horizontal), vertical responses to DV-axis translation (DV-vertical), and both horizontal and vertical responses to NO-axis oscillation (1.5 and 5 Hz). Observations focus on responses to 5-Hz oscillations, in which visual inputs are essentially ineffective in modifying the LVOR. 4. The kinematics of perfect ocular compensation during head translation indicate that the ideal ocular response is governed by the motion of the eye relative to target position. Relevant variables include target distance, which is crucial for all axes of motion, and target eccentricity, which is important only for head motion roughly parallel to the target (NO-axis translation). Findings are compatible with predictions based on ideal kinematics. However, it is the point of binocular fixation in space, not actual target position, that governs LVOR behavior. 5. The IA-horizontal and DV-vertical LVOR is in response to head motion roughly orthogonal to the line of sight. Responses under all stimulus conditions (LVOR, VSLVOR, and VLVOR) behaved similarly at 5 Hz, and were modulated linearly with vergence [in meter angles (MA), the reciprocal of binocular fixation distance].(ABSTRACT TRUNCATED AT 400 WORDS)