Visual tracking of moving targets requires the combination of smooth pursuit eye movements with catch-up saccades. In primates, catch-up saccades usually take place only during pursuit initiation because pursuit gain is close to unity. This contrasts with the lower and more variable gain of smooth pursuit in cats, where smooth eye movements are intermingled with catch-up saccades during steady-state pursuit. In this paper, we studied in detail the role of retinal slip in the prediction of target motion during smooth and saccadic pursuit in the cat. We found that the typical pattern of pursuit in the cat was a combination of smooth eye movements with saccades. During smooth pursuit initiation, there was a correlation between peak eye acceleration and target velocity. During pursuit maintenance, eye velocity oscillated at approximately 3 Hz around a steady-state value. The average gain of smooth pursuit was approximately 0.5. Trained cats were able to continue pursuing in the absence of a visible target, suggesting a role of the prediction of future target motion in this species. The analysis of catch-up saccades showed that the smooth-pursuit motor command is added to the saccadic command during catch-up saccades and that both position error and retinal slip are taken into account in their programming. The influence of retinal slip on catch-up saccades showed that prediction about future target motion is used in the programming of catch-up saccades. Altogether, these results suggest that pursuit systems in primates and cats are qualitatively similar, with a lower average gain in the cat and that prediction affects both saccades and smooth eye movements during pursuit.