Propagating waves are observed in the olfactory or procerebral (PC) lobe of the terrestrial mollusk, Limax maximus. Wave propagation is altered by cutting through the various layers of the PC lobe both parallel and transverse to the direction of wave propagation. We present a model for the PC lobe based on two layers of coupled cells. The top layer represents the cell layer of the PC lobe, and the bottom layer corresponds to the neuropil of the PC lobe. To get wave propagation, we induce a coupling gradient so that the most apical cells receive a greater input from neighbors than the basal cells. The top layer in the model is composed of oscillators coupled locally, whereas the bottom layer is comprised of oscillators with global coupling. Odor stimulation is represented by an increase in the strength of coupling between the two layers. This model allows us to explain a number of experimental observations: 1) the intact PC lobe exhibits regular propagating waves, which travel from the apical to the basal end; 2) there is a gradient in the local frequency of slices cut transverse to the axis of wave propagation, with apical slices oscillating faster than basal slices; 3) with partial cuts through the cell layer or the neuropil layer, the apical and basal ends remain tightly coupled; 4) removal of the neuropil layer does not prevent wave propagation in the cell layer; 5) odor stimulation causes the waves to collapse and the cells in the PC lobe oscillate synchronously; and 6) by allowing a single parameter to vary in the model, we capture the reversal of waves in low chloride medium.