The differential equations governing the unsteady motion of a system of two superimposed liquids are integrated by use of the method of characteristics. The solution differs significantly from that obtained by assuming a very thin lower layer. If the basic shear across the interface is small, a wave breaks forward (as an ordinary water wave) only if the amplitude is fairly small and if the lower layer is thinner than the upper layer. If the upper fluid is thinner, the wave breaks backward. The speed of the various points of the wave does not vary monotonically with amplitude. If a shear exists, higher velocities in the upper layer in the direction of wave propagation favor the forward breaking of a wave. The opposite shear may cause a wave to break backward.