We investigated the extent to which the human visual system can detect discontinuities in first-order optical flow fields. We constructed two types of spatial discontinuities: a circular split field with a straight edge and a disk with annular surround. We used two different first-order optical flow components: an expansion and a rotation. We found an intriguing difference in the detection thresholds for straight and circular discontinuities. Whereas straight discontinuities yielded thresholds of 10%-50% difference in expansion or rotation, circular discontinuities could, at first, only be detected at extreme differences (≫100%). After a learning period, thresholds for such stimuli decreased, but they remained significantly higher than thresholds for the straight edge. Thresholds rose for stimuli that formed a gradual transition between a circular and a straight edge, and they decreased with increasing eccentricity of the circular discontinuity. Results suggest that symmetry in the stimulus, defined by the coincidence of the center of expansion or rotation and the center of the circular discontinuity, was responsible for the difference in thresholds for circular and straight discontinuities.