1. The effects of lesions in both human and nonhuman primates have implicated the cerebellum in the control of rapid eye movements, i.e., saccades. To examine the neural substrate of this control, we recorded the discharge patterns of cerebellar output cells in the fastigial nucleus while monkeys tracked a small, jumping spot of light. 2. In the caudal fastigial nucleus, neurons discharged for saccades in one or several directions. All exhibited a burst. Some also exhibited a saccade-related pause in firing either before or after saccades greater than approximately 3-5-degrees. Thirty-seven percent discharged only a burst, 44% also exhibited a pause before bursts in certain directions, and 19% also paused after the saccade-related burst in certain directions. Although many cells discharged steadily during intersaccadic intervals, few exhibited a robust relation between firing rate and eye position. 3. As a measure of directional selectivity, we plotted the burst lead time as a function of saccade direction for saccades of similar (10-degrees) radial amplitudes. Of 20 neurons tested, 17 burst earliest for contralateral saccades and 1 for upward saccades; 2 others showed little dependence on direction. Of 19 additional units tested only in the horizontal direction, 18 burst earlier for contralateral saccades. 4. For contralateral saccades the burst preceded saccades of all sizes by at least 7.7 ms on average. For ipsilateral saccades, the burst preceded small saccades by an average of 10.3 ms. However, as ipsilateral saccade size increased, the burst began later and later relative to saccade onset so that, on average, it always occurred after the onset of 20-degrees saccades but well before the saccade ended. 5. Many fastigial saccade-related units showed increases in the number of spikes with saccade size and in burst duration with saccade duration in one or more directions. For either relation the highest average correlation coefficients ranged from 0.6 to 0.65. In general, the average correlation coefficients and slopes for either relation were slightly larger for contralateral saccades. Pure burst neurons did not display better average correlations than neurons that also paused. For neurons that also paused either before or after saccades, there was a weak tendency for pause duration to increase with the duration of larger saccades. 6. We tested the effect of eye position on unit discharge in 13 cells by requiring the monkey to make 10-degrees ipsilateral and contralateral saccades from a variety of starting positions. Eight of the neurons exhibited clear qualitative differences in either the burst characteristics, the presence of an accompanying pause, or the intersaccadic steady firing rate for different starting positions. However, only 2 of the 13 exhibited at least 1 correlation coefficient between burst parameters and starting position of 0.8 or more; 7 additional cells had at least 1 coefficient in excess of 0.4. The correlations with starting position did not improve when we sorted saccades into centrifugal and centripetal movements. 7. The saccade-related discharge of fastigial neurons was anything but machinelike. For some units, saccades of the same size and starting position were accompanied by bursts of widely differing frequencies and durations. In addition, alertness and/or attention appeared to affect the saccadic responses. 8. Nevertheless, our data suggest that the fastigial nucleus is involved in helping to accelerate contralateral saccades and in helping to decelerate ipsilateral ones. If this is true, lesions of the fastigial nucleus should cause contralateral saccades to become hypometric and ipsilateral saccades to become hypermetric. The pharmacological inactivations of the fastigial nucleus reported in the companion paper produced just such deficits.