When presented with locally paired dots moving in opposite directions, motion selective neurons in the middle temporal cortex (MT) reduce firing while neurons in V1 are unaffected. This physiological effect is known as motion opponency. The current study used psychophysics to investigate the neural circuit underlying motion opponency. We asked whether opposing motion signals could arrive from different eyes into the receptive field of a binocular neuron while still maintaining motion opponency. We took advantage of prior findings that orientation discrimination of the motion axis (along which paired dots oscillate) is harder when dots move counter-phase than in-phase, an effect associated with motion opponency. We found that such an effect disappeared when paired dots originated from different eyes. This suggests that motion opponency, at some point, involves strictly monocular processing. This does not mean that motion opponency is entirely monocular. Further, we found that the effect of a Glass pattern disappeared under similar viewing conditions, suggesting that Glass pattern perception also involves some strictly monocular processing.