The motions of overlapping contours in a visual scene may arise from the physical motion(s) of either a single or multiple surface(s). A central problem facing the visual motion system is that of assigning the most likely interpretation. The rules underlying this perceptual decision can be explored using a visual stimulus formed by superimposing two moving gratings. The resultant percept is either that of a single coherently moving 'plaid pattern' (coherent motion) or of the two component gratings sliding noncoherently across one another (noncoherent motion). When plaid patterns are configured to mimic one transparent grating overlying another, the percept of noncoherent motion dominates. We now report that neurons in the visual cortex of rhesus monkeys exhibit changes in direction tuning that parallel this perceptual phenomenon: sensitivity to the motions of the component gratings is enhanced under conditions that favour the perception of noncoherent motion. These results challenge models of cortical visual processing that fail to take into account the contribution of figural image segmentation cues to the analysis of visual motion.