We examined perceptual coherence of two-component moving plaids. The gratings which 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 which generate a compelling percept of motion even though they fail to elicit a motion signal from motion analyzers based on standard cross-correlation (Chubb and Sperling 1988). Naive observers viewed three types of stimuli consisting of superpositions of these two components: (i) two standard drifting gratings (F/F), (ii) two non-Fourier drifting gratings (NF/NF), and (iii) 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 observers for the NF/NF stimulus was one of coherent motion, provided that both gratings were visible and of approximately equal contrast. No observer 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 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.