In primates, one type of retinal ganglion cell, the parasol cell, makes gap junctions with amacrine cells, the inhibitory, local circuit neurons. To study the effects of these gap junctions, we developed a linear, mathematical model of the retinal circuitry providing input to parasol cells. Electrophysiological studies have indicated that gap junctions do not enlarge the receptive field centres of parasol cells, but our results suggest that they make other contributions to their light responses. According to our model, the coupled amacrine cells enhance the responses of parasol cells to luminance contrast by disinhibition. We also show how a mixed chemical and electrical synapse between two sets of amacrine cells presynaptic to the parasol cells might make the responses of parasol cells more transient and, therefore, more sensitive to motion. Finally, we show how coupling via amacrine cells can synchronize the firing of parasol cells. An action potential in a model parasol cell can excite neighbouring parasol cells, but only when the coupled amacrine cells also fire action potentials. Passive conduction was ineffective due to low-pass temporal filtering. Inhibition from the axons of the coupled amacrine cells also produced oscillations that might synchronize the firing of more distant ganglion cells.