The mechanisms of conscious perception have been studied for many years using bistable visual stimuli, which result in switches of perceptual interpretation during viewing, despite a lack of physical change in the stimulus characteristics. Theoretical studies have identified potential neural mechanisms such as neural adaptation, inhibitory competition, and noise, as key components that lead to switches in perception, while neurophysiological studies have identified brain responses and brain areas that appear to be critical to switches in perception. Compared to vision, bistable perception in other modalities is less well understood, although studies on bistable auditory perception performed thus far indicate more similarities than differences with visual bistable perception. We used functional magnetic resonance imaging to study brain activity around the time of switches in perception while participants were listening to a bistable auditory stream segregation stimulus, which can be heard as one integrated stream of pure tones or two segregated streams of tones. The auditory thalamus showed more activity around the time of a switch from segregated to integrated compared to stable perception of integrated; in contrast, the rostral-anterior cingulate cortex and the inferior parietal lobule showed more activity around the time of a switch from integrated to segregated compared to time periods of stable perception of segregated streams, consistent with prior findings of asymmetries in brain activity depending on switch direction. In sound-responsive areas in the auditory cortex, neural activity declined in strength over time following switches in perception, but increased in strength preceding switches in perception. Such dynamics in auditory cortex are consistent with the role of adaptation proposed by computational models of visual and auditory bistable switching, whereby the strength of neural activity decreases in strength following a switch in perception, which eventually destabilizes the current percept enough to lead to a switch to an alternative percept.