We present a model for the temporal integration of apparent motion information. The model is constructed by considering psychophysical and neurophysiological data, and consists of the leaky integration of pulsatile motion detector responses to apparent motion stimuli. Each pulse represents a motion detector populational response to a discrete spatial displacement of the spatial pattern. Temporal contrast sensitivity determines the shape of constant-stimulus-duration threshold curves for image frame exposure durations less than about 133 msec. The shape of the threshold curve for image frame exposure durations greater than about 133 msec is determined by the leaky integrator time constant and the shape of the pulses emitted by the motion detectors. The leaky integrator model exhibits threshold saturation behaviour (the reaching of a maximum sensitivity or minimum threshold) seen in psychophysical data as well as dependence of saturation time on the frame rate of the apparent motion stimulus. A low frame rate results in a longer time-to-saturation because the leaky integrator discharges more between detector output pulses. When the motion detector output pulses are far enough apart there is effectively no temporal integration and therefore no threshold improvement over time. Finally, the behaviour of the psychophysical threshold curves across spatial displacement sizes is consistent with a populational-response threshold mechanism combined with spatial summation over a non-uniform distribution of detector types across the visual field.