Binocular rivalry occurs when different images are presented one to each eye: the images are visible only alternately. Monocular rivalry occurs when different images are presented both to the same eye: the clarity of the images fluctuates alternately. Could both sorts of rivalry reflect the operation of a general visual mechanism for dealing with perceptual ambiguity? We report four experiments showing similarities between the two phenomena. First, we show that monocular rivalry can occur with complex images, as with binocular rivalry, and that the two phenomena are affected similarly by the size (Experiment 1) and colour (Experiment 2) of the images. Second, we show that the distribution of dominance periods during monocular rivalry has a gamma shape and is stochastic (Experiment 3). Third, we show that during periods of monocular-rivalry suppression, the threshold to detect a probe (a contrast pulse to the suppressed stimulus) is raised compared with during periods of dominance (Experiment 4). The threshold elevation is much weaker than during binocular rivalry, consistent with monocular rivalry’s weak appearance. We discuss other similarities between monocular and binocular rivalry, and also some differences, concluding that part of the processing underlying both phenomena is a general visual mechanism for dealing with perceptual ambiguity.