A novel random-dot stereogram (RDS) was used to study stereoscopic motion. For this RDS stimulus, the direction of luminance motion and the direction of the moving cyclopean pattern can be independently controlled. The perceived cyclopean motion was examined under five different conditions, in which the cyclopean pattern was moving either up or down, the luminant dots were: (1) moving in the cyclopean direction; (2) moving opposite to the cyclopean direction; (3) moving orthogonal to the cyclopean direction, (4) stationary; or (5) dynamic (dots uncorrelated in successive frames). The study showed that luminance direction dominated cyclopean direction and that smooth and coherent cyclopean motion is seen only if luminance motion is present. The results suggest that stereoscopic motion is processed by interactions between separate binocular disparity units and luminance motion units, and not by a single binocular motion system, in which binocular units are tuned to both disparity and direction of motion.