A numerical analysis of the transport properties and the chemical stability of bilayer membranes with the compositions La0.9Sr0.1FeO3/Ce0.8Gd0.2O2 and La1-xSrxCoO3/Ce0.8Gd0.2O2 was carried out. For each membrane layer, the oxygen permeation flux was derived as a function of the defect concentrations and defect mobilities. The defect concentrations were calculated from point defect models. Coupling of the flux equations via the continuity condition yields the overall permeation flux of the bilayer membrane and the oxygen chemical activity at the layer interface, which serves as a criterion for the stability of the membrane under reducing conditions.