1. We recorded single-unit activity from neurons of an output of the cerebellum, the fastigial nucleus, in two rhesus macaques while the monkeys tracked small moving targets with their eyes. Many neurons in the caudal part of the fastigial nucleus exhibited a modulation in their discharge rates when smooth-pursuit eye movements were elicited by either sinusoidal or step-ramp motions of a small target. 2. The pursuit direction that elicited the most vigorous modulation in unit firing to sinusoidal target motion could be horizontal, vertical, or oblique. Most often, the preferred direction was in the contralateral and/or downward direction (50 of 69 neurons) or in the ipsilateral and/or upward direction (13 of 69). 3. For units whose preferred smooth-pursuit directions were either contralateral/downward or ipsilateral/upward during sinusoidal pursuit, peak firing as measured by the phase shift of periodic modulation at 0.5-0.8 Hz occurred near the time of peak velocity. The discharge of 80% of the neurons with contralateral/downward preferred directions preceded eye velocity by an average of -27 degrees; thus these neurons discharged maximally during eye acceleration. In contrast, neurons with ipsilateral/upward preferred directions lagged peak velocity by an average of +10.5 degrees and therefore discharged during eye deceleration. 4. The average eye velocity sensitivity for sinusoidal pursuit between 0.5 and 0.8 Hz was 0.83 +/- 0.57 (SD) spikes/s per degrees/s. We also tested 36 units during pursuit at a variety of frequencies in their preferred directions and found that firing rates increased monotonically with peak eye velocity. However, the firing rate saturated at velocities ranging from 20 to 60 degrees/s for different units. 5. When a monkey tracked a step-ramp target motion, three discharge patterns emerged in the 27 units tested. Just over half of the units discharged a burst of spikes that preceded (average lead of 27.4 +/- 17 ms) and lasted throughout the initial third of the eye acceleration; the burst was followed by a subsequent steady firing that continued after the eye had accelerated to its steady velocity. Fewer neurons discharged a burst that began late in the acceleration and was followed by steady firing. Occasional neurons showed only a gradual increase in firing rate during acceleration followed by a steady discharge. 6. Thirty of the 31 fastigial smooth-pursuit units tested also were modulated during sinusoidal yaw and/or pitch oscillations while the animals fixated a spot that rotated with them.(ABSTRACT TRUNCATED AT 400 WORDS)