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]. Regression of pooled data yielded a slope of 0.22-degrees.cm-1.MA-1 and intercept (response at O MA) of 0.45-degrees.cm, compared with the ideal slope of 0.57-degrees.cm-1.MA-1 and intercept of zero. The positive intercept may be useful by providing better response compensation at modest vergence angles than if the intercept were zero. 6. The NO-LVOR entails head motion roughly parallel to the line of sight. Horizontal and vertical responses were observed that were modulated independently with fixation characteristics. LVOR, VSLVOR, and VLVOR responses at 5 Hz were nearly absent when gaze was parallel to the NO axis but increased in amplitude independently with gaze eccentricity and vergence. The direction of response depended on the direction of gaze; during forward head motion the eyes moved upward during up-gaze, downward during down-gaze, rightward during right-gaze, and leftward during left-gaze. The LVOR during 5 Hz NO-axis head motion also included a vergence LVOR. Its amplitude was appropriately modulated with ambient vergence angle. This implies a form of response dissociation between the two eyes. When binocular fixation converged between the eyes, right and left horizontal LVOR responses opposed each other. 7. The IA-horizontal, DV-vertical, and NO-axis LVORs show characteristics consistent with the kinematics of ideal compensatory eye movements. Important attributes of compensatory LVORs include 1) responses are properly directed and temporally synchronized relative to head translation, 2) response amplitudes rise as binocular fixation distance shortens, and 3) responses to high-frequency NO-axis oscillation are modulated in amplitude and sign depending on gaze angle as well as by fixation distance. Evidence supports the notion that the point of binocular fixation is determined internally by signals proportional to gaze and vergence angles (although a role for accommodation is not ruled out) and that these signals in turn modulate the VOR commensurate with kinematic requirements. Actual target (visual) input is not directly relevant at high frequencies (e.g., 5 Hz), but is presumably used to guide the point of binocular fixation to coincide with target position under most natural conditions.