Infants gradually learn to predict the motion of moving targets and change from a strategy that mainly depends on saccades to one that depends on anticipatory control of smooth pursuit. A model is described that combines three types of mechanisms for gaze control that develops in a way similar to infants. Initially, gaze control is purely reactive, but as the anticipatory models become more accurate, the gain of the pursuit will increase and lead to a larger fraction of smooth eye movements. Finally, a third system learns to predict changes in target motion, which will lead to fast retuning of the parameters in the anticipatory model.