There is considerable evidence for the existence of a specialized mechanism in human vision for detecting moving contrast modulations and some evidence for a mechanism for detecting moving stereoscopic depth modulations. It is unclear whether a single second-order motion mechanism detects both types of stimulus or whether they are detected separately. We show that sensitivity to stereo-defined motion resembles that to contrast-defined motion in two important ways. First, when a missing-fundamental disparity waveform is moved in steps of 0.25 cycles, its perceived direction tends to reverse. This is a property of both luminance-defined and contrast-defined motion and is consistent with independent detection of motion at different spatial scales. Second, thresholds for detecting the direction of a smoothly drifting sinusoidal disparity modulation are much higher than those for detecting its orientation. This is a property of contrast-modulated gratings but not luminance-modulated gratings, for which the two thresholds are normally identical. The results suggest that stereo-defined and contrast-defined motion stimuli are detected either by a common mechanism or by separate mechanisms sharing a common principle of operation.