The permeabilities of glassy polymers to various gases depend on the feed pressure. The dependence of permeability on feed pressure for glassy polymers has been widely characterized on the basis of the dual-mode sorption and transport model for the case of a vacuum permeate pressure. Non-zero permeate pressures are more typical in practical separation systems. In this study we analyze and characterize the dependence of permeability on the permeate pressure for a glassy polyimide. Nonzero permeate pressures are shown to depress the selectivity of the carbon dioxide-methane system, because the permeability of the carbon dioxide is depressed more than the permeability of methane. The significance of these observations for membrane characterization and permeator design is discussed. Measurements of the selectivity of mixed gas feeds for a glassy polyimide were made with a constant permeate pressure. These data are compared and interpreted in terms of the dual-mode model and the contributions of the so-called "frame of reference" to the apparent permeability and selectivity.