Biological visual systems can detect positional changes that are finer than these systems' acuity to sine-wave gratings, a property known as hyperacuity. Some systems can even detect changes finer that the photoreceptor spacing. We report here that rabbit's directionally selective ganglion cells not only detect positional changes in the hyperacuity range, but also discriminate the direction of their motion. Our experiments show that directional selectivity occurs for edges of light moving as little as 1.1 microns (26" of visual angle) across the retina. This distance corresponds to a hyperacuity, since the acuity to sine-wave gratings of rabbit's On-Off DS ganglion cells is about 125 microns (50'). In addition, this distance is smaller than the minimal spacing between rabbit photoreceptors (1.9 microns or 46"), as estimated from cell-density studies (Young & Vaney, 1991). Such a hyperacuity suggests low-noise high-gain signal transmission from photoreceptors to ganglion cells and that directional selectivity can arise in small portions of retinal dendritic processes.