When different images are presented to the two eyes, they compete for perceptual dominance, such that one image is visible while the other is suppressed. This binocular rivalry is thought to reflect competition between monocular neurons within the primary visual cortex. However, neurons whose activity correlates with perception during rivalry are found mainly in higher cortical areas, and respond to input from both eyes. Thus rivalry may involve competition between alternative perceptual interpretations at a higher level of analysis. To investigate this, we tested the effect of rapidly alternating the rival stimuli between the two eyes. Under these conditions, the perceptual alternations exhibit the same temporal dynamics as with static patterns, and a single phase of perceptual dominance can span multiple alternations of the stimuli. Thus neural representations of the two stimuli compete for visual awareness independently of the eye through which they reach the higher visual areas. This finding places binocular rivalry in the general category of multistable phenomena, such as ambiguous figures, and provides a new way to study the neural cause and resolution of perceptual ambiguities.