This study models the network interactions of five classes of neurons in the crayfish retina which support lateral inhibition and directional selectivity. The models approximate pulse responses and responses to drifting sinusoidal gratings in each cell type. Lateral inhibition is implemented by a shunting inhibitory feedback from lamina amacrine cells to the photoreceptor terminals. This mechanism determines the range of possible spatial and temporal frequencies of the synaptic input signals to the transmedullary and tangential cells. Tangential cells implement a delay and compare operation via competitive binding of GABA and ACh to ligand-gated membrane channels. The delay and compare operation can account for the directional selectivity which is observed experimentally in the tangential cells but not in any of the cells which form its input pathway. The models presented are nonlinear. They can reproduce the observed pulse responses over wide range of light intensities.