When the visual system is confronted with incompatible images in the same part of the visual field, the conscious percept switches back and forth between the rivaling stimuli. Such spontaneous flips provide important clues to the neuronal basis for visual awareness. The general idea is that two representations compete for dominance in a process of mutual inhibition, in which adaptation shifts the balance to and fro. The inherent nonlinear nature of the rivalrous flip-flop and its stochastic behavior, however, made it impossible to disentangle inhibition and adaptation. Here we report a general method to measure the time course, and asymmetries, of mechanisms involved in perceptual rivalry. Supported by model simulations, we show the dynamics of opponent interactions between mutual inhibition and adaptation. The findings not only provide new insight into the mechanism underlying rivalry but also offer new opportunities to study and compare a wide range of bistable processes in the brain and their relation to visual awareness.