The stability, with respect to quasi-geostrophic disturbances, of flows containing both horizontal and vertical shear is studied, as a continuation of a previous paper. Bounds are placed on the phase speed of neutral waves and necessary conditions for the existence of marginally stable waves are derived for the two-layer system. These conditions show how, for the two-layer model, a classification of flows is possible on the basis of allowable marginally stable waves. The classification distinguishes flows with potential vorticity extrema within a layer from those with no such extrema. The stability of particular flows illustrating the classes of flows is examined in detail. Those unstable waves occurring in a current with no extremum are shown to be potential-energy converting while they increase the kinetic energy of the mean flow. Waves which owe their existence to a potential vorticity extremum appear to be similar to barotropic, kinetic-energy converting waves which reduce the kinetic energy of the mean flow.