We present an analysis of the Wagon Wheel Illusions--classic psychophysical phenomena--in the context of a neural network model of orientation selectivity in the visual system. We find that both the continuous Wagon Wheel Illusion (c-WWI) and the standard, stroboscopic Wagon Wheel Illusion (WWI) can be explained by a recurrent model in which the cortex provides both excitatory and inhibitory feedback to a weakly tuned input from the lateral geniculate nucleus. Comparison of data from recent psychophysics experiments with theoretical predictions derived from the network dynamics leads to excellent agreement. Conversely, this agreement confirms the validity of the model and highlights the fact that the Wagon Wheel Illusion can serve as a useful probe of the human striate cortex. We find that the WWI results from phase-locking in the visual system and that a circle map determines the dynamics of the illusion. Furthermore, our results suggest that the c-WWI is a consequence of continuous processing and cannot be used to support claims of discrete processing by the visual system.