Step-ramp target motion evokes a characteristic sequence of presaccadic smooth eye movement in the direction of the target ramp, catch-up targets to bring eye position close to the position of the moving target, and postsaccadic eye velocities that nearly match target velocity. I have analyzed this sequence of eye movements in monkeys to reveal a strong postsaccadic enhancement of pursuit eye velocity and to document the conditions that lead to that enhancement. Smooth eye velocity was measured in the last 10 ms before and the first 10 ms after the first saccade evoked by step-ramp target motion. Plots of eye velocity as a function of time after the onset of the target ramp revealed that eye velocity at a given time was much higher if measured after versus before the saccade. Postsaccadic enhancement of pursuit was recorded consistently when the target stepped 3 degrees eccentric on the horizontal axis and moved upward, downward, or away from the position of fixation. To determine whether postsaccadic enhancement of pursuit was invoked by smear of the visual scene during a saccade, I recorded the effect of simulated saccades on the presaccadic eye velocity for step-ramp target motion. The 3 degrees simulated saccade, which consisted of motion of a textured background at 150 degrees/s for 20 ms, failed to cause any enhancement of presaccadic eye velocity. By using a strategically selected set of oblique target steps with horizontal ramp target motion, I found clear enhancement for saccades in all directions, even those that were orthogonal to target motion. When the size of the target step was varied by up to 15 degrees along the horizontal meridian, postsaccadic eye velocity did not depend strongly either on the initial target position or on whether the target moved toward or away from the position of fixation. In contrast, earlier studies and data in this paper show that presaccadic eye velocity is much stronger when the target is close to the center of the visual field and when the target moves toward versus away from the position of fixation. I suggest that postsaccadic enhancement of pursuit reflects activation, by saccades, of a switch that regulates the strength of transmission through the visual-motor pathways for pursuit. Targets can cause strong visual motion signals but still evoke low presaccadic eye velocities if they are ineffective at activating the pursuit system.