The activity of 176 individual cells in the arm area of motor cortex (areas 4 and 6) was studied while monkeys made arm movements of similar direction within different parts of extrapersonal space. The behavioral paradigm used was a 3-dimensional reaction-time task aimed at dissociating the direction of movement, which remained similar across the work space, from the patterns of muscular activity and the angular joint excursions necessary to perform these movements. In agreement with other studies (Georgopoulos et al., 1982; Schwartz et al., 1988), we found that, within a given part of space, the activity of 169 (96.0%) cells studied increased most for a given preferred direction and less for other directions of movement. This change was graded in an orderly fashion. We further analyzed the orientation in space of the cells' preferred directions under the differing conditions of the task. We found that, as movements with similar trajectories were made within different parts of space, the cells' preferred directions changed spatial orientation. This change was of different magnitudes for different cells, but at the level of the population, it followed closely the changes in orientation of the arm necessary to perform the movements required by the task. Movement population vectors (Georgopoulos et al., 1983, 1986, 1988) computed from cell activity proved to be good predictors of movement direction regardless of where in space the movements were performed. These results indicate that motor cortical cells can code direction of movement in a way which is dependent on the position of the arm in space. The data are discussed in relation to the existence of mechanisms which facilitate the transformation between extrinsic and intrinsic coordinates. These transformations are necessary to perform arm movements to visual targets in space.