Measurements of visual tracking in infants have been performed from 2 weeks of age. Although directed appropriately, the eye movements are saccadic at this age. Over the first 4 months of life, a rapid transition to successively smoother eye movements takes place. Timing develops first and at 7 weeks of age the smooth pursuit is well timed to a sinusoidal motion of 0.25 Hz. From this age, the gain of the smooth pursuit improves rapidly and from 4 months of age, smooth pursuit dominates visual tracking in combination with head movements. This development reflects massive cortical and cerebellar changes. The coordination between eyes-head-body and the external events to be tracked presumes predictive control. One common type of model for explaining the acquisition of such control focuses on the maturation of the cerebellar circuits. A problem with such models, however, is that although Purkinje cells and climbing fibers are present in the newborn, the parallel and mossy fibers, essential for predictive control, grow and mature at 4-7 months postnatally. Therefore, an alternative model that also includes the prefrontal cerebral cortex might better explain the early development of predictive control. The prefrontal cortex functions by 3-4 months of age and provides a site for prediction of eye movements as a part of cerebro-cerebellar nets.