Ocular following responses (OFRs) are the initial tracking eye movements that can be elicited at ultra-short latency by sudden motion of a textured pattern. A recent study used motion stimuli consisting of two large coextensive sine-wave gratings with the same orientation but different spatial frequency and moving in (1/4)-wavelength steps in the same or opposite directions: when the two gratings differed in contrast by more than about an octave then the one with the higher contrast completely dominated the OFR and the one with lower contrast lost its influence as though suppressed [Sheliga, B. M., Kodaka, Y., FitzGibbon, E. J., & Miles, F. A. (2006). Human ocular following initiated by competing image motions: Evidence for a winner-take-all mechanism. Vision Research, 46, 2041-2060]. This winner-take-all (WTA) outcome was attributed to nonlinear interactions in the form of mutual inhibition between the mechanisms sensing the competing motions. In the present study, we recorded the initial horizontal OFRs to the horizontal motion of two vertical sine-wave gratings that differed in spatial frequency and were each confined to horizontal strips that extended the full width of our display (45 degrees ) but were only 1-2 degrees high. The two gratings could be coextensive or separated by a vertical gap of up to 8 degrees , and each underwent motion consisting of successive (1/4)-wavelength steps. Initial OFRs showed strong dependence on the relative contrasts of the competing gratings and when these were coextensive this dependence was always highly nonlinear (WTA), regardless of whether the two gratings moved in the same or opposite direction. When the two gratings moved in opposite directions the nonlinear interactions were purely local: with a vertical gap of 1 degrees or more between the gratings OFRs approximated the linear sum of the responses to each grating alone. On the other hand, when the two gratings moved in the same direction the nonlinear interactions were more global: even with a gap of 8 degrees -the largest separation tried-OFRs were still substantially less than predicted by the linear sum. When the motions were in the same direction, we postulate two nonlinear interactions: local mutual inhibition (resulting in WTA) and global divisive inhibition (resulting in normalization). Motion stimuli whose responses were totally suppressed by coextensive opponent motion of higher contrast were rendered invisible to normalization, suggesting that the local interactions responsible for the WTA behavior here occur at an earlier stage of neural processing than the global interactions responsible for normalization.