The spatial and temporal interactions in the receptive fields of On-Off directionally selective (DS) ganglion cells endow them with directional selectivity. Using a variety of stimuli, such as sinusoidal gratings, we show that these interactions make directional selectivity of the DS ganglion cell robust with respect to stimulus parameters such as contrast, speed, spatial frequency, and extent of motion. Moreover, unlike the directional selectivity of striate-cortex cells, On-Off DS ganglion cells display directional selectivity to motions not oriented perpendicularly to the contour of the objects. We argue that these cells may achieve such high robustness by combining multiple mechanisms of directional selectivity.