The integration of visual information is a critical task that is performed by neurons in the extrastriate cortex of the primate brain. For motion signals, integration is complicated by the geometry of the visual world, which renders some velocity measurements ambiguous and others incorrect. The ambiguity arises because neurons in the early stages of visual processing have small receptive fields, which can only recover the component of motion perpendicular to the orientation of a contour (the aperture problem). Unambiguous motion signals are located at end points and corners, which are referred to as terminators. However, when an object moves behind an occluding surface, motion measurements made at the terminators formed by the intersection of the object and the occluder are generally not consistent with the direction of object motion. To study how cortical neurons integrate these different motion cues, we used variations on the classic "barber pole" stimulus and measured the responses of neurons in the middle temporal area (MT or V5) of extrastriate cortex of alert macaque monkeys. Our results show that MT neurons are more strongly influenced by the unambiguous motion signals generated by terminators than to the ambiguous signals generated by contours. Furthermore, these neurons respond better to terminators that are intrinsic to a moving object than to those that are accidents of occlusion. V1 neurons show similar response patterns to local cues (contours and terminators), but for large stimuli, they do not reflect the global motion direction computed by MT neurons. These observations are consistent with psychophysical findings that show that our perception of moving objects often depends on the motion of terminators.