Nonlinear, multiplication-like operations carried out by individual nerve cells greatly enhance the computational power of a neural system, but our understanding of their biophysical nature is scant. We pursue this problem in the Drosophila ON motion vision circuit, where we record the membrane potentials of direction-selective T4 neurons and of all their columnar input elements in response to visual and pharmacological stimuli in vivo. Our electrophysiological measurements and conductance-based simulations suggest a passive supralinear interaction between two distinct types of synapse on T4 dendrites. We show that this multiplication-like operation arises from the coincidence of cholinergic excitation and release from glutamatergic inhibition. The latter depends on the expression of the glutamate-gated chloride channel GluClα in T4 neurons, which sharpens the cells’ directional tuning and shapes the animals’ optomotor behaviour. Interacting pairs of shunting inhibitory and excitatory synapses have long been postulated as a way of implementing an analogue version of a logic AND gate, which is integral to theories of motion detection, sound localization, and sensorimotor control.