The initial ocular following responses (OFRs) elicited by 1/4-wavelength steps applied to the missing fundamental (mf) stimulus are in the backward direction and largely determined by the principal Fourier component, the 3rd harmonic [Sheliga, B. M., Chen, K. J., FitzGibbon, E. J., & Miles, F. A. (2005). Initial ocular following in humans: A response to first-order motion energy. Vision Research, 45, 3307-3321]. When the contrast of the 3rd harmonic was selectively reduced below that of the next most prominent harmonic-the 5th, which moves in the opposite (forward) direction-then the OFR reversed direction and the 3rd harmonic effectively lost all of its influence as the OFR was now largely determined by the 5th harmonic. Restricting the stimulus to just two sine waves (of equal efficacy when of equal contrast and presented singly) with the spatial frequencies of the 3rd and 5th harmonics of the mf stimulus indicated that the critical factor was the ratio of their two contrasts: when of similar contrast both were effective (vector sum/averaging), but when the contrast of one was <1/2 that of the other then the one with the lower contrast became ineffective (winner-take-all). This nonlinear dependence on the contrast ratio was attributed to mutual inhibition and was well described by a weighted-average model with just two free parameters. Further experiments with broadband and dual-grating stimuli indicated that nonlinear interactions occur not only in the neural processing of stimuli moving in opposite directions but also of stimuli that share the same direction and differ only in their spatial frequency and speed. Clearly, broad-band and dual-grating stimuli can uncover significant nonlinearities in visual information processing that are not evident with single sine-wave stimuli.