1. Three rhesus monkeys were trained to perform a rapid (greater than 100 degrees/s) and a slow (less than 100 degrees/s) wrist movement guided by a visual cue. While the monkey performed wrist flexion or extension from a neutral position, Purkinje cell (P-cell) discharges were recorded from intermediate and lateral parts of lobules IV--VI of the cerebellum. 2. By the visually guided movement, we could control the direction of the wrist movement; the holding position at three different angles of the wrist joint: neutral, about 30 degrees flexed, and extended; and the velocity in four ranges: a) 10--30, b) 30--100, c) 100--300, and d) 300-650 degrees/s. 3. From 92 P-cells that significantly increased or decreased the discharge rate of simple spikes with task performance, we selected 45 P-cells ("response-locked" cells) as related to the wrist movement by statistical analyses of temporal correlation of P-cell activities to wrist movement. The direction of the frequency modulation (increase or decrease) was in a nonreciprocal fashion with oppositely directed wrist movements (flexion or extension) in 90% of the response-locked P-cells. The maintained frequencies at three holding positions did not significantly differ. 4. Nineteen P-cells changed their spike frequencies temporally locked to both rapid and slow wrist movements. By the discharge pattern in relation to the rapid and slow movements, these cells were classified into two groups. Discharge pattern in group I P-cells (n = 5) conformed very well to that of velocity, and a linear correlation between the instantaneous increase of the discharge rate and velocity was observed in analyses of individual trials. Group II cells showed increase (n = 9) or decrease (n = 5) of firing rate (20--50 spikes/s) larger than group I cells (less than 10 spikes/s) as long as the wrist was moving, even with very slow velocity (less than 30 degrees/s. The correlations between the increase of the discharge rate and the velocity in individual trials were less clear in group II than in group I cells. 5. The present study suggests the importance of the cerebellar cortex in controlling the slow limb movement as well as the rapid movement. The selected P-cells in this study also suggested that the velocity or some dynamic aspect related to the velocity of limb movement is the major information among the dissociated motion parameters coded by the simple-spike frequencies of the P-cells in the cerebellar hemisphere. Whether the latter suggestion represents an essential characteristic of all limb movement-related P-cells or reflects only a feature of a special subgroup among the movement-related cells should be clarified in future experiments.