We have previously reported a transparent motion after-effect indicating that the human visual system comprises separate slow and fast motion channels. Here, we report that the presentation of a fast motion in one eye and a slow motion in the other eye does not result in binocular rivalry but in a clear percept of transparent motion. We call this new visual phenomenon 'dichoptic motion transparency' (DMT). So far only the DMT phenomenon and the two motion after-effects (the 'classical' motion after-effect, seen after motion adaptation on a static test pattern, and the dynamic motion after-effect, seen on a dynamic-noise test pattern) appear to isolate the channels completely. The speed ranges of the slow and fast channels overlap strongly and are observer dependent. A model is presented that links after-effect durations of an observer to the probability of rivalry or DMT as a function of dichoptic velocity combinations. Model results support the assumption of two highly independent channels showing only within-channel rivalry, and no rivalry or after-effect interactions between the channels. The finding of two independent motion vision channels, each with a separate rivalry stage and a private line to conscious perception, might be helpful in visualizing or analysing pathways to consciousness.