The nonlinear stability of plane Poiseuille-Couette flow is analyzed at large Reynolds number. An asymptotic self-sustaining structure is found which involves the interaction of two nonlinear critical layers with near-wall Stokes regions. A global property of the flow-field, involving the vorticity of the mean-flow distortion, is used to determine the amplitude dependence of the O(1) wavenumber and phasespeed and it is found that solutions exist for values of wall sliding speed considerably in excess of the linear cut-off. In the situation where the phasespeed is almost equal to the wall sliding speed, a new nonlinear structure arises involving critical layer/shear layer interaction. The numerical results from this latter interaction are found to compare well with full solutions of the Navier-Stokes equations.