1. The role of the paravermal cerebellum in controlling arm movements in monkeys trained to perform visually guided movements was investigated. Discharge patterns of extracellularly recorded Purkinje, Golgi, nuclear and unidentified cells were correlated with arm position, velocity and acceleration. 2. The discharge of thirty-seven out of fifty-two movement-related Purkinje cells and that of thirty-three out of forty-five other movement-related cerebellar neurones was more highly correlated with limb velocity (0.95 greater than r greater than 0.4) than with position or acceleration. Twelve out of fifty-two Purkinje cells and twelve out of forty-five other cells were related to both limb velocity and limb position. Three Purkinje cells were related to limb acceleration and position and no cell was related to position or acceleration alone. 3. Modulation of discharge of these cells usually preceded movement (range -240 ms, unit leading movement, to +180 ms, unit lagging; mode -36 ms; mean -15 ms). 4. Each movement-related neurone was tested for four directions of movement. All showed a preferred direction in which the correlation with arm movement velocity was highest. However, 43% (30/70) correlated at r greater than 0.4 with movements in a second direction, usually that opposite to their preferred direction. Sixty-three per cent of these neurones fired earlier during movements in the preferred than in the opposite direction. 5. It is concluded that the paravermal cerebellum may be involved in computing the velocity vectors required for achieving properly directed and co-ordinated movements of the whole arm.