Ambiguous stimuli can produce spontaneous perceptual alternations in the mind of the observer, even though the stimulus itself remains the same. Common features in the temporal dynamics of bistability have been observed for various types of stimuli, both visual and auditory. This raises the question of whether bistable perception results from stereotyped, local competition between stimulus-specific representations or whether it is triggered by some central, supramodal mechanism. We tested the distributed versus centralized hypothesis by asking observers to simultaneously monitor their bistable perception of ambiguous auditory and visual stimuli. Strong interactions between auditory and visual perceptual switches would indicate a central decision mechanism. We used streaming stimuli in the auditory modality and either plaids or apparent motion stimuli in the visual modality. The use of two different sensory modalities allowed the distinction of contextual interactions due to the similarity between stimuli from interactions linked to perceptual decision itself. The long-term dynamics of bistable perception were identical in unimodal and bimodal presentations for all types of stimuli. Surprisingly, even strong short-term cross-modal interactions, when present, did not alter these dynamics. We conclude that bistability can co-occur independently in different sensory modalities. This observation supports models of distributed competition for perceptual decision and awareness.