Brief movements of a large-field visual stimulus elicit short-latency tracking eye movements termed "ocular following responses" (OFRs). To address the question of whether OFRs can be elicited by purely binocular motion signals in the absence of monocular motion cues, we measured OFRs from monkeys using dichoptic motion stimuli, the monocular inputs of which were flickering gratings in spatiotemporal quadrature, and compared them with OFRs to standard motion stimuli including monocular motion cues. Dichoptic motion did elicit OFRs, although with longer latencies and smaller amplitudes. In contrast to these findings, we observed that other types of motion stimuli categorized as non-first-order motion, which is undetectable by detectors for standard luminance-defined (first-order) motion, did not elicit OFRs, although they did evoke the sensation of motion. These results indicate that OFRs can be driven solely by cortical visual motion processing after binocular integration, which is distinct from the process incorporating non-first-order motion for elaborated motion perception. To explore the nature of dichoptic motion processing in terms of interaction with monocular motion processing, we further recorded OFRs from both humans and monkeys using our novel motion stimuli, the monocular and dichoptic motion signals of which move in opposite directions with a variable motion intensity ratio. We found that monocular and dichoptic motion signals are processed in parallel to elicit OFRs, rather than suppressing each other in a winner-take-all fashion, and the results were consistent across the species.