In the natural environment, we often form stable perceptual experiences from ambiguous and fleeting sensory inputs. Which neural activity underlies the content of perception and which neural activity supports perceptual stability remains an open question. We used a bistable perception paradigm involving ambiguous images to behaviorally dissociate perceptual content from perceptual stability, and magnetoencephalography to measure whole-brain neural dynamics in humans. Combining multivariate decoding and neural state-space analyses, we found frequency-band-specific neural signatures that underlie the content of perception and promote perceptual stability, respectively. Across different types of images, non-oscillatory neural activity in the slow cortical potential (<5 Hz) range supported the content of perception. Perceptual stability was additionally influenced by the amplitude of alpha and beta oscillations. In addition, neural activity underlying perceptual memory, which supports perceptual stability when sensory input is temporally removed from view, also encodes elapsed time. Together, these results reveal distinct neural mechanisms that support the content versus stability of visual perception.