A central problem in motor research has been to understand how sensory signals are transformed to generate a goal-directed movement. This problem has been formulated as a set of coordinate transformations that begins with an extrinsic coordinate frame representing the spatial location of a target and ends with an intrinsic coordinate frame describing muscle activation patterns. Insight into this process of sensorimotor transformation can be gained by examining the coordinate frames of neuronal activity in interconnected regions of the brain. We recorded the activity of neurons in primary motor cortex (M1) and ventral premotor cortex (PMv) in a monkey trained to perform a task which dissociates three major coordinate frames of wrist movement: muscle, wrist joint, and an extrinsic coordinate frame. We found three major types of neurons in M1 and PMv. The first type was termed 'extrinsic-like'. The activity of these neurons appeared to encode the direction of movement in space independent of the patterns of wrist muscle activity or joint movement that produced the movements. The second type was termed 'extrinsic-like with gain modulation'. The activity of these neurons appeared to encode the direction of movement in space, but the magnitude (gain) of neuronal activity depended on the posture of the forearm. The third type was termed 'muscle-like' since their activity co-varied with muscle activity. The great majority of the directionally-tuned neurons in the PMv were classified as 'extrinsic-like' (48/59, 81%). A smaller group was classified as 'extrinsic-like with gain modulation' (7/59, 12%). In M1, the three types of neurons were more equally represented. Our results raise the possibility that cortical processing between M1 and PMv may contribute to a sensorimotor transformation between extrinsic and intrinsic coordinate frames. Recent modeling studies have demonstrated the computational plausibility of such a process.