The stability of Rossby waves in a two-layer fluid on a β-plane is examined. There are four parameters in the problem, (a)M =UK2/β whereUis the velocity amplitude of the particular wave being considered andKis its wavenumber, (b)F= (Kac)−2whereacis the baroclinic radius of deformation, (c) the depth ratio δ =H1/H2whereH1andH2are the mean thicknesses of the upper and lower layer, respectively, and (d) the wave direction.