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Diverse sensory systems, from audition to thermosensation, feature a separation of inputs into ON (increments) and OFF (decrements) signals. In the Drosophila visual system, separate ON and OFF pathways compute the direction of motion, yet anatomical and functional studies have identified some crosstalk between these channels. We used this well-studied circuit to ask whether the motion computation depends on ON-OFF pathway crosstalk. Using whole-cell electrophysiology, we recorded visual responses of T4 (ON) and T5 (OFF) cells, mapped their composite ON-OFF receptive fields, and found that they share a similar spatiotemporal structure. We fit a biophysical model to these receptive fields that accurately predicts directionally selective T4 and T5 responses to both ON and OFF moving stimuli. This model also provides a detailed mechanistic explanation for the directional preference inversion in response to the prominent reverse-phi illusion. Finally, we used the steering responses of tethered flying flies to validate the model's predicted effects of varying stimulus parameters on the behavioral turning inversion.