In the primary visual cortex (V1), it has been shown that the neuronal response elicited by a grating patch in the receptive field (RF) center can be suppressed or facilitated by an annular grating presented in the RF surround area; the effect depends on the relative orientations of the two gratings. The effect is thought to play a role in figure-ground segregation. Here we have found that response modulation similar to that reported in cortical area V1 can also be found in all major classes of retinal ganglion cells (RGCs), including "concentric" cells. Orientation-specific response modulation of this kind cannot result from interactions of independent RF mechanisms; therefore more complex mechanism, which takes into account the relative orientations of the gratings in the RF center and surround, or sensing the borders between texture regions, has to be present in RFs of RGCs, even of the concentric type. This challenges the consensus notion that their responses to visual stimuli are governed entirely by a RF composed of separate mechanisms: center, antagonistic surround, and modulatory extraclassical surround. Our findings raise the question of whether initial stages of complex analysis of visual input, normally attributed to the visual cortex, can be achieved within the retina.