Neural adaptation and inhibition are pervasive characteristics of the primate brain and are probably understood better within the context of visual processing than with any other sensory modality. These processes are thought to underlie illusions in which one motion affects the perceived direction of another, such as the direction aftereffect (DAE) and direction repulsion. The DAE describes how, following prolonged viewing of motion in one direction, the direction of a subsequently viewed test pattern is misperceived. In the case of direction repulsion, the direction difference between two transparently moving surfaces is overestimated. Explanations of the DAE appeal to neural adaptation, whereas direction repulsion is accounted for through lateral inhibition. Here, we report on a new illusion, the binary DAE (bDAE), in which superimposed slow and fast dots moving in the same direction are perceived to move in different directions following adaptation to a mixed-speed stimulus. This new phenomenon is essentially a combination of the DAE and direction repulsion. Interestingly, the magnitude of the bDAE is greater than would be expected simply through a linear combination of the DAE and direction repulsion, suggesting that the mechanisms underlying these two phenomena interact in a nonlinear fashion.