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Our eyes are never still, but tend to "freeze" in response to stimulus onset. This effect is termed "oculomotor inhibition" (OMI); its magnitude and time course depend on the stimulus parameters, attention, and expectation. We previously showed that the time course and duration of microsaccade and spontaneous eye-blink inhibition provide an involuntary measure of low-level visual properties such as contrast sensitivity during fixation. We investigated whether this stimulus-dependent inhibition also occurs during smooth pursuit, for both the catch-up saccades and the pursuit itself. Observers followed a target with continuous back-and-forth horizontal motion while a Gabor patch was briefly flashed centrally with varied spatial frequency and contrast. Catch-up saccades of the size of microsaccades had a similar pattern of inhibition as microsaccades during fixation, with stronger inhibition onset and faster inhibition release for more salient stimuli. Moreover, a similar stimulus dependency of inhibition was shown for pursuit latencies and peak velocity. Additionally, microsaccade latencies at inhibition release, peak pursuit velocities, and latencies at minimum pursuit velocity were correlated with contrast sensitivity. We demonstrated the generality of OMI to smooth pursuit for both microsaccades and the pursuit itself and its close relation to the low-level processes that define saliency, such as contrast sensitivity.