Responses of single neurons in cat visual cortex were measured in response to sinewave grating stimuli. Firstly, a neuron's spatial frequency tuning was determined, and subsequent stimuli were set at the optimal spatial frequency for that neuron. Then a "jumping grating" stimulus was used: a sinewave grating subjected to a series of abrupt spatial displacements, while remaining stationary for a fixed exposure time between displacements. The amount of direction selectivity elicited by this stimulus was measured as a function of the amount of spatial displacement. Visual cortex neurons generally showed an optimal spatial displacement, corresponding to somewhat less than one quarter of a spatial period of the neuron's optimal spatial frequency (close to, but systematically less than, "quadrature phase"). In a majority of neurons tested, this optimal displacement was not affected by increasing the exposure time between displacements, indicating that the measurements were not a simple consequence of temporal frequency tuning. These results closely parallel recent human psychophysical data obtained from measurements of motion aftereffect or direction discrimination elicited by jumping grating stimuli.