Many neurons in the dorsal region of the medial superior temporal area (MSTd) of monkey cerebral cortex respond to optic flow stimuli in which the center of motion is shifted off the center of the visual field. Each shifted-center-of-motion stimulus presents both different directions of planar motion throughout the visual field and a unique pattern of global motion across the visual field. We investigated the contribution of planar motion to the responses of these neurons in two experiments. In the first, we compared the responses of 243 neurons to planar motion and to shifted-center-of-motion stimuli created by vector summation of planar motion and radial or circular motion. We found that many neurons preferred the same directions of motion in the combined stimuli as in the planar stimuli, but other neurons did not. When we divided our sample into one group with stronger directionality to both planar and vector combination stimuli and one group with weaker directionality, we found that the neurons with the stronger directionality were those that showed the greatest similarity in the preferred direction of motion for both the planar and combined stimuli. In a second set of experiments, we overlapped planar motion and radial or circular motion to create transparent stimuli with the same motion components as the vector combination stimuli, but without the shifted centers of motion. We found that the neurons that responded most strongly to the planar motion when it was combined with radial or circular motion also responded best when the planar motion was overlapped by a transparent motion stimulus. We conclude that the responses of those neurons with stronger directional responses to both the motion of planar and vector combination stimuli are most readily understood as responding to the total planar motion in the stimulus, a planar motion mechanism. Other neurons that had weaker directional responses showed no such similarity in the preferred directions of planar motion in the vector combination and the transparent overlap stimuli and fit best with a mechanism dependent on the global motion pattern. We also found that neurons having significant responses to both radial and circular motion also responded to the spiral stimuli that result from a vector combination of radial and circular motion. The preferred planar-spiral vector combination stimulus was frequently the one containing that neurons' preferred direction of planar motion, which makes them similar to other MSTd neurons.