We study pressure-driven, two-layer flow in inclined channels with high density and
viscosity contrasts. We use a combination of asymptotic reduction, boundary-layer theory and the
Karman-Polhausen approximation to derive evolution equations that describe the interfacial dynamics.
Two distinguished limits are considered: where the viscosity ratio is small with density
ratios of order unity, and where both density and viscosity ratios are small. The evolution equations
account for the presence of inertia, gravity, capillarity and viscous retardation; attention is
restricted to situations in which the flow is laminar. The results of our linear stability analysis and
numerical simulations indicate that the flow is destabilised by positive channel inclination in the
stably stratified case. The dependence of the nonlinear wave dynamics on system parameters is
also explored.