We examine two-layer geostrophic flows over a flat bottom on the β-plane. If the displacement of the interface is of the order of the depth of the upper layer, the dynamics of the flow depends on the following non-dimensional parameters:(i)the Rossby number ε,(ii)the ratio δ of the depth of the upper layer to the total depth of the fluid,(iii)the “β-effect number” α = Ro/Recot , where Rois the deformation radius, Re, is the earth's radius and is the latitude. In this paper