We analyze the dynamic properties of a neural network model for on-off spiking neurons recorded in the first optic chiasm of the fly visual system. The model consists of two parallel pathways and three sequential processing stages. The first stage models photoreceptors. At the second stage, the signal is segregated into on- and off-pathways. These pathways are proposed to correspond to two populations of amacrine cells. At the third stage, the on- and off-pathways converge to on-off neurons. Furthermore, according to the model, on-off neurons interact via recurrent connections. This stage is proposed to correspond to lamina L4 neurons. In response to luminance increments and decrements, the model exhibits a three-component response and suggests pathways for each of the components. When stimulated by a train of pulses, the model exhibits fast adaptation for frequencies higher than about 5 Hz. Furthermore, adaptation to on- and off-pulses occurs independently. When the frequency of stimulation is reduced, the unit recovers rapidly from its adapted state. The temporal modulation transfer function has its peak around 7 Hz. The phase characteristics show a phase lead for low temporal frequencies changing to a phase lag for high frequencies. These model predictions are compared with data from Jansonius and van Hateren (1991).