Following previous studies documenting the ability to generate anticipatory responses, we tested whether the repeated motion of a visual target along the same path affected its oculomotor tracking. In six rhesus monkeys, we evaluated how the frequency of a target path influenced the onset, the accuracy and velocity of eye movements. Three hundred milliseconds after its extinction, a central target reappeared and immediately moved toward the periphery in four possible (oblique) directions and at constant speed (20 or 40°/s). During each daily sessions, the frequency of one motion direction was either uncertain (25% of trials) or certain (100% of trials). Our results show no reduction of saccade latency between the two sessions. No express saccades were observed in either session. A slow eye movement started after target onset (pre-saccadic glissade) and its velocity was larger during the “certain” sessions only with the 40°/s target. No anticipatory eye movement was observed. Longer intersaccadic intervals were found during the “certain” sessions but the post-saccadic pursuit velocity exhibited no change. No correlation was found between the accuracy and precision of saccades (interceptive or catch-up) and the post-saccadic pursuit velocity. Repeatedly tracking a target that moves always along the same path does not favor the generation of anticipatory eye movements, saccadic or slow. Their occurrence is not spontaneous but seems to require a preliminary training. Finally, for both sessions, the lack of correlation between the saccade-related and pursuit-related kinematic parameters is consistent with separate control of saccadic and slow eye movements.