Psychophysical studies have demonstrated that humans are less sensitive to image acceleration than to image speed (e.g., Gottsdanker, 1956; Werkhoven, Snippe, & Toet, 1992). Because there is evidence that a common motion-processing stage subserves perception and pursuit (e.g., Watamaniuk & Heinen, 1999), either pursuit should be similarly impaired in discriminating acceleration or it must receive input from a system different from the one that processes visual motion for perception. We assessed the sensitivity of pursuit to acceleration or speed, and compared the results with those obtained in perceptual experiments done with similar stimuli and tasks. Specifically, observers pursued or made psychophysical judgments of targets that moved at randomly selected base speeds and subsequent accelerations. Oculomotor and psychophysical discrimination were compared by analyzing performance for the entire stimulus set sorted by either target acceleration or speed. Thresholds for pursuit and perception were higher for target acceleration than speed, further evidence that a common motion-processing stage limits the performance of both systems.