Moving objects are often occluded by neighboring objects. In order for the eye to smoothly pursue a moving object that is transiently occluded, a prediction of its trajectory is necessary. For targets moving on a linear path, predictive eye velocity can be regulated on the basis of target motion before and after the occlusions. However, objects in a more dynamic environment move along more complex trajectories. In this condition, a dynamic internal representation of target motion is required. Yet, the nature of such an internal representation has never been investigated. Similarly, the impact of predictive saccades on the predictive smooth pursuit response has never been considered. Therefore, we investigated the predictive smooth pursuit and saccadic responses during the occlusion of a target moving along a circular path. We found that the predictive smooth pursuit was driven by an internal representation of target motion that evolved with time. In addition, we demonstrated that in two dimensions, the predictive smooth pursuit system does influence the amplitude of predictive saccades but not vice versa. In conclusion, in the absence of retinal inputs, the smooth pursuit system is driven by the output of a short-term velocity memory that contains the dynamic representation of target motion.