When we fixate the center of a rotating three-dimensional structure, such as a physically rotating wheel made out of sectors, which stereo cues are encoded with a static random-dot “texture,” a rather striking global motion illusion occurs: the rotating three-dimensional wheel appears as standing still (stereo rotation standstill). Even when using a dynamic (flickering) random-dot texture, it is still impossible to gain a percept of smooth rotation. However, local motion can still be clearly perceived. When the random-dot texture “overlaying” the wheel is also rotating, the concealed wheel is perceived as rotating at the same velocity as the texture, regardless of its velocity (stereo rotation capture). Stereo complex motion standstill and capture is shown to occur for other categories of complex motions such as expanding, contracting, and spiraling motions thus providing evidence for a dominance of luminance inputs over stereo inputs for complex motion detectors in our visual system.