The presentation of saccadic and smooth pursuit eye movements as two separate systems has recently been reconsidered: The two subsystems share a number of anatomical structures, and recent data suggest that this sharing also extends to physiological processes. The aim of our study was first to test whether these two subsystems share a common predictive process. We designed a new predictive smooth pursuit paradigm that requires the triggering of unpredictable saccades, performed either during low (ongoing pursuit) or high (pursuit direction reversal) predictive behavior. Saccade latency was used as a probe to reveal a possible sharing of prediction between the two subsystems. The main finding was that saccade latencies were markedly decreased when triggered around pursuit direction reversal and performed in the direction of the predicted pursuit. The aim of the second part of this study was to determine the neural substrate of this common predictive process. According to previous studies, the supplementary eye field (SEF) would be involved in the control of predictive pursuit. The same subjects therefore performed the same tasks, and transcranial magnetic stimulation (TMS) was applied over this area: Decreased saccade latencies were no longer observed, whereas it continued to be observed when applied over the occipital cortex. These results are consistent with (1) The existence of a common predictive process shared by both oculomotor subsystems; (2) The view of the SEF not as a primary oculomotor area but as a higher order structure able to elaborate complex processes, such as prediction, independently of the oculomotor output.