We studied the binocular organization of motion opponency and its relationship to contrast gain control. Luminance contrast thresholds for discriminating direction of motion were measured for drifting Gabor patterns (target) presented on counterphase flickering Gabor patterns (pedestal). There were four presentation conditions: binocular, monocular, dichoptic, and half-binocular. For the half-binocular presentation, the target was presented to one eye while pedestals were presented to both eyes. In addition, to test for motion opponency, we studied two increment and decrement conditions, in which the target increased contrast for one direction of movement but decreased it for the opposite moving component of the pedestal. Threshold versus pedestal contrast functions showed a dipper shape, and there was a strong interaction between pedestal contrast and test condition. Binocular thresholds were lower than monocular thresholds but only at low pedestal contrasts. Monocular and half-binocular thresholds were similar at low pedestal contrasts, but half-binocular thresholds became higher and closer to dichoptic thresholds as pedestal contrast increased. Adding the decremental target reduced thresholds by a factor of two or more-a strong sign of opponency-when the decrement was in the same eye as the increment or the opposite eye. We compared several computational models fitted to the data. Converging evidence from the present and previous studies (Gorea, Conway, & Blake, 2001) suggests that motion opponency is most likely to be monocular, occurring before direction-specific binocular summation and before divisive, binocular gain control.