We examined the perceptual coherence of two-component moving plaids. The gratings that constituted the plaids were either standard Fourier gratings (F), in which luminance was determined by a drifting sinusoid, or non-Fourier gratings (NF), in which the contrast of a random background was modulated by a drifting sinusoid. These NF gratings are examples of stimuli that generate a compelling percept of motion, even though they fail to elicit a motion signal from motion analyzers based on standard cross-correlation (Chubb & Sperling, 1988). Naive observers viewed three types of stimuli consisting of superpositions of these two components: (1) two standard drifting gratings (F/F), (2) two non-Fourier drifting gratings (NF/NF), and (3) one standard and one non-Fourier drifting grating (F/NF). As expected, the F/F stimulus yielded a compelling percept of coherent motion. The dominant percept of all the observers for the NF/NF stimulus was one of coherent motion, provided that both gratings were visible and of approximately equal contrast. None of the observers reported a dominant percept of coherent motion for the F/NF condition, over a wide range of contrasts for the two grating components and across two varieties of NF gratings. In view of the results of Albright (1992) and Albright and Chaudhuri (1989), that show that single cells in macaque V1 and MT respond to both F and NF motion, one cannot interpret our findings as evidence that F and NF motion are processed independently. Alternative, "higher level" interpretations based on the intrinsically ambiguous nature of the stimuli and physical laws governing the appearance of transparent objects are discussed.