1. The purpose of this study was to quantify the response characteristics of eye movements produced by linear head oscillations in the dark (the linear vestibuloocular reflex, or LVOR). Horizontal, vertical, and torsional eye movements were measured in adult squirrel monkeys by the use of a dual scleral search-coil technique during linear oscillations (0.5, 1.5, and 5.0 Hz, 0.36 g peak acceleration) along the animals' interaural (IA), dorsoventral (DV), and nasooccipital (NO) axes. 2. Two LVOR responses, horizontal eye movements during IA-axis translation and vertical eye movements during DV-axis motion, were in a compensatory direction for head translation. Response amplitudes increased as frequency increased, whereas phase typically showed a lead. 3. Two other LVORs, torsional responses during IA-axis translation (all frequencies) and vertical responses during NO-axis oscillations (0.5 Hz), behaved differently. These two LVORs cannot be functionally compensatory for head translation because they degrade fixation on targets, and therefore image stability, by rotating the eyes off target (NO-vertical) or torting the eyes relative to the visual world (IA-torsional). Responses to NO-axis motion at frequencies greater than 0.5 Hz depended on initial eye position and fixation distance and are described in the companion paper. 4. The effect of head orientation on the LVOR was assessed by testing four head positions in 90 degrees steps around the axis of head motion for each of the three axes of translation. This was done, first, to determine whether the LVORs are responses to the "swinging vector" of gravitoinertial force during linear head motion or to head translation; and second, to quantify potential effects of static head (otolith) orientation on the LVORs. Results showed no systematic effects of head orientation on LVOR responses in the frequency bandwidth studied. This indicates that the LVORs are dependent on the direction of linear motion relative to the head (and otolith organs) but not on the swinging vector of gravitoinertial force, and that the LVORs are uninfluenced by static orientation of the head and reloading of the otoliths.