We describe the relations between the neuronal activity in primate motor cortex and the direction of arm movement in three-dimensional (3- D) space. The electrical signs of discharge of 568 cells were recorded while monkeys made movements of equal amplitude from the same starting position to 8 visual targets in a reaction time task. The layout of the targets in 3-D space was such that the direction of the movement ranged over the whole 3-D directional continuum in approximately equal angular intervals. We found that the discharge rate of 475/568 (83.6%) cells varied in an orderly fashion with the direction of movement: discharge rate was highest with movements in a certain direction (the cell's "preferred direction") and decreased progressively with movements in other directions, as a function of the cosine of the angle formed by the direction of the movement and the cell's preferred direction. The preferred directions of different cells were distributed throughout 3-D space. These findings generalize to 3-D space previous results obtained in 2-D space (Georgopoulos et al., 1982) and suggest that the motor cortex is a nodal point in the construction of patterns of output signals specifying the direction of arm movement in extrapersonal space.