Animals, from invertebrates to humans, stabilize the panoramic optic flow through compensatory movements of the eyes, the head or the whole body, a behavior known as optomotor response (OR). The same optic flow moved clockwise or anticlockwise elicits equivalent compensatory right or left turning movements, respectively. However, if stimulated monocularly, many animals show a unique effective direction of motion, i.e., a unidirectional OR. This phenomenon has been reported in various species from mammals to birds, reptiles, and amphibious, but among invertebrates, it has only been tested in flies, where the directional sensitivity is opposite to that found in vertebrates. Although OR has been extensively investigated in crabs, directional sensitivity has never been analyzed. Here, we present results of behavioral experiments aimed at exploring the directional sensitivity of the OR in two crab species belonging to different families: the varunid mud crab Neohelice granulata and the ocypode fiddler crab Uca uruguayensis. By using different conditions of visual perception (binocular, left or right monocular) and direction of flow field motion (clockwise, anticlockwise), we found in both species that in monocular conditions, OR is effectively displayed only with progressive (front-to-back) motion stimulation. Binocularly elicited responses were directional insensitive and significantly weaker than monocular responses. These results are coincident with those described in flies and suggest a commonality in the circuit underlying this behavior among arthropods. Additionally, we found the existence of a remarkable eye dominance for the OR, which is associated to the size of the larger claw. This is more evident in the fiddler crab where the difference between the two claws is huge.