Nonlinear wave propagation is ubiquitous in nature, appearing in chemical reaction kinetics, cardiac tissue dynamics, cortical spreading depression and slow wave sleep. The application of dynamical modelling has provided valuable insights into the mechanisms underlying such nonlinear wave phenomena in several domains. Wave propagation can also be perceived as sweeping waves of visibility that occur when the two eyes view radically different stimuli. Termed binocular rivalry, these fluctuating states of perceptual dominance and suppression are thought to provide a window into the neural dynamics that underlie conscious visual awareness. Here we introduce a technique to measure the speed of rivalry dominance waves propagating around a large, essentially one-dimensional annulus. When mapped onto visual cortex, propagation speed is independent of eccentricity. Propagation speed doubles when waves travel along continuous contours, thus demonstrating effects of collinear facilitation. A neural model with reciprocal inhibition between two layers of units provides a quantitative explanation of dominance wave propagation in terms of disinhibition. Dominance waves provide a new tool for investigating fundamental cortical dynamics.