To compensate for neural delays, organisms require predictive motor control. We investigated the transition between reaction and prediction in saccades (rapid eye movements) to periodically paced targets. Tracking at low frequencies (0.2-0.3 Hz) is reactive (eyes lag target) and at high frequencies (0.9-1.0 Hz) is predictive (eyes anticipate target); there is an abrupt rather than smooth transition between the two modes (a "phase transition," as found in bistable physical systems). These behaviors represent stable modes of the oculomotor control system, with attendant rapid switching between the neural pathways underlying the different modes. Furthermore, predictive saccades exhibit long-term correlations (slow decay of the autocorrelation function, manifest as a 1/f alpha spectrum). This indicates that predictive trials are not independent. The findings have implications for the understanding of predictive motor control: predictive performance during a given trial is influenced by a feedback process that takes into account the latency of previous trials.