Recent physiological findings revealed that about one-third of motion-sensitive neurons in the pigeon's pretectal nucleus encoded the acceleration of visual motion. Here we propose a microcircuit hypothesis, in which the slow adaptive depressions play a significant role in response generating, to account for the origin of the three important properties of the acceleration-sensitive neurons: the plateau-shaped speed-tuning curves, the opposite-signed after-responses (OSARs) and the acceleration sensitivities. The flat plateau within the speed-tuning curves and the OSARs to motion offset observed in experiments are reproduced successfully in simulations, and the simulative responses of the acceleration-sensitive neurons to step changes, ramp changes in stimulus speed and sine wave modulations of stimulus speed are qualitatively consistent with physiological observations. Thus, a biologically plausible substrate for the neurons' classification and the origin of the three propert...