Two-phase gas-liquid flows are important in a variety of heat transfer systems, such as in the on-chip cooling of microelectromechanical devices up to the infrastructure of safety systems in nuclear power plants. We focus on the case of two-layer flows in inclined channels, where a gas and a liquid, immiscibly separated by a sharp interface with large surface tension, flow in opposite directions. The liquid is driven by gravity while the gas flows due to an imposed pressure gradient. For disturbance wavelengths that are much longer than the channel thickness, a fourth-order nonlinear equation which describes the evolution of the separating interfacial shape is found that is coupled to an elliptic equation for the pressure, whose solution provides a constraint to the dynamics of the flow. We survey the impact of these different constraints on the solutions, and extend the analysis to include incompressibility effects. This work was a collaboration with T.M. Segin and L. Kondic.