In the natural world, the brain must handle inherent delays in visual processing. This is a problem particularly during dynamic tasks. A possible solution to visuo-motor delays is prediction of a future state of the environment based on the current state and properties of the environment learned from experience. Prediction is well known to occur in both saccades and pursuit movements and is likely to depend on some kind of internal visual model as the basis for this prediction. However, most evidence comes from controlled laboratory studies using simple paradigms. In this study, we examine eye movements made in the context of demanding natural behavior, while playing squash. We show that prediction is a pervasive component of gaze behavior in this context. We show in addition that these predictive movements are extraordinarily precise and operate continuously in time across multiple trajectories and multiple movements. This suggests that prediction is based on complex dynamic visual models of the way that balls move, accumulated over extensive experience. Since eye, head, arm, and body movements all co-occur, it seems likely that a common internal model of predicted visual state is shared by different effectors to allow flexible coordination patterns. It is generally agreed that internal models are responsible for predicting future sensory state for control of body movements. The present work suggests that model-based prediction is likely to be a pervasive component in natural gaze control as well.