An object moving in the visual field triggers a saccade that brings its image onto the fovea. It is followed by a combination of slow pursuit eye movements and catch-up saccades that keep the target image onto the fovea as long as possible. The accuracy of this ability to track the “here-and-now” location of a target contrasts with the distributed nature of the encoding processes in the brain and the variable sensorimotor delays. We studied how this performance is acquired in 6 inexperienced rhesus monkeys that we recorded during consecutive sessions. During the early exposure, the tracking is surprisingly mostly saltatory, made of saccades separated by low eye velocity episodes, demonstrating that smooth pursuit is not a spontaneous response to a moving stimulus. A joint evolution of saccade and pursuit components is observed. Across sessions, the tracking becomes less discontinuous and the smooth pursuit more prominent. This smoothing is observed at several scales, across the time course of each trial, trial repetitions and consecutive training sessions. We explain how saccades facilitate the evolution of smooth pursuit, even in the absence of stringent training constraints. Our findings create new perspectives for studying in the oculomotor system the neural mechanisms underlying implicit visuomotor learning and synchronization.