Although motion parallax is closely associated with observer head movement, the underlying neural mechanism appears to rely on a pursuit-like eye movement signal to disambiguate perceived depth sign from the ambiguous retinal motion information [Naji, J. J., & Freeman, T. C. A. (2004). Perceiving depth order during pursuit eye movement. Vision Research, 44, 3025-3034; Nawrot, M. (2003). Eye movements provide the extra-retinal signal required for the perception of depth from motion parallax. Vision Research, 43, 1553-1562]. Here, we outline the evidence for a pursuit signal in motion parallax and propose a simple neural network model for how the pursuit theory of motion parallax might function within the visual system. The first experiment demonstrates the crucial role that an extra-retinal pursuit signal plays in the unambiguous perception of depth from motion parallax. The second experiment demonstrates that identical head movements can generate opposite depth percepts, and even ambiguous percepts, when the pursuit signal is altered. The pursuit theory of motion parallax provides a parsimonious explanation for all of these observations.