When each eye is confronted with a dissimilar stimulus, the percept will generally alternate between the two. This phenomenon is known as binocular rivalry. Although binocular rivalry occurs at locations where targets overlap spatially, the area surrounding rivalrous targets can modulate their dominance. Here we show that during binocular rivalry of oppositely moving gratings, a surrounding grating moving in the same direction as one of the two leads to increased dominance of the opposite direction of motion in the center. This increased dominance of the opposite direction in the center was observed irrespective of the eye to which the surround was presented. Inspection of the results for different conditions reveals that the preference for the opposite direction of motion cannot be explained by a single mechanism operating beyond binocular fusion. We therefore suggest that this phenomenon is the outcome of center-surround interactions at multiple levels along the pathway of visual motion processing.