1. Extracellular recordings were obtained from 124 Purkinje cells (P-cells) in the flocculus of alert monkeys. P-cell simple spike-firing rate was analyzed quantitatively during various combinations of smooth-pursuit eye movement and passive head rotation. 2. During sinusoidal smooth eye movements, 80% of the P-cells displayed increased firing rate during ipsilateral and 20% during contralateral eye movement. Over the frequency range 0.3--1.4 Hz, firing-rate modulation was proportional to and in phase with maximum eye velocity. During the steady state of triangle-wave tracking, firing rate increased monotonically as a function of eye velocity. Since firing rate was uncorrelated with retinal-error velocity, one component of P-cell firing rate was related to eye velocity. 3. During the transient phase of triangle-wave tracking, when an instantaneous change in the direction of target movement caused a large retinal-error velocity, 40% of the P-cells were related only to eye velocity. Sixty percent of the P-cells displayed an overshoot or undershoot in firing rate, indicating a relationship to either retinal-error velocity or eye acceleration as well as to eye velocity. 4. During the vestibuloocular reflex (VOR), evoked by head rotation in the dark, P-cell firing rate was only weakly modulated. In contrast, when the monkey suppressed the VOR by fixating a target that rotated with him, P-cell rate was deeply modulated. Since the modulation was proportional to and in phase with maximum head velocity, another component of P-cell firing rate was related to head velocity. 5. Of 36 P-cells tested, 35 displayed firing-rate modulation during both suppression of the VOR and smooth-pursuit eye movement. P-cells that reached peak firing rate during ipsilateral head rotation also reached peak firing rate during ipsilateral smooth eye rotation. Average population sensitivitites to head velocity and eye velocity were equal. In three conditions in which eye and head velocity were elicited simultaneously, P-cell firing rate could be predicted by the linear, vector addition of the separate eye and head velocity components of firing rate. Therefore, the relatively weak modulation of P-cell firing rate during the VOR in the dark can be accounted for by the cancellation of equal but opposite head and eye velocity components. 6. The connections of flocculus P-cells to interneurons in the brain stem VOR pathways have been established in other mammals. In the context of those connections, P-cell firing patterns were appropriate to facilitate the eye movements the monkey was required to make. We conclude that the flocculus is important for sustaining any smooth eye movements that are different from those evoked by head rotation in the dark. The eye velocity component may represent an efference copy signal that sustains ongoing eye velocity during smooth pursuit.