Successful foveation of a dynamic target depends on good predictions of its movement direction and speed. We measured and compared the temporal dynamics of directional precision of both saccades and smooth pursuit and their interactions. We also compared the directional precision of both eye movements to psychophysical direction discrimination thresholds. Directional thresholds of pure pursuit responses improved rapidly and reached asymptotic values of 1.5°-3° within 300 ms after target motion onset, both for trained and untrained observers and irrespective of the speed of the stimuli. Psychophysical thresholds were in the same range. Directional thresholds for saccades in the ramp paradigm were just slightly higher, but these occurred significantly earlier in time at around 200 ms after target motion onset. At the equivalent time during pure pursuit initiation, thresholds were typically higher by 2°-3°. The rise in directional precision-or decrease in thresholds-over time was more pronounced for trials with longer latencies. As an effect, precision depended mainly on time since stimulus motion onset rather than pursuit onset. Directional precision for saccades to static targets was slightly better than to moving targets, at even shorter latencies. We conclude that directional precision is higher for the saccadic system at saccade onset than for the pursuit system, presumably due to additional position signals that are not available to the pursuit system at that point in time. The pursuit response improves rapidly due to refined sensory processing and motor planning. The combination of initial saccades and pursuit to track moving targets is a good strategy for the oculomotor system to reduce directional errors during the phase of initiation. The target speed has very little effects on the directional precision of both eye movements.