A membrane reactor with separate reactants feed for the catalytic combustion of propane was studied in the transition from the kinetics- to the transport-controlled regime, where a clear steady-state multiplicity phenomenon takes place. The experimental data were interpreted through a model which takes the mass and heat transfer inside and outside the membrane into account. The external heat transfer towards the cooling surfaces of the reactor and the uneven catalyst distribution over the membrane were identified as the most important features governing the behaviour of the reactor. The good agreement between the model predictions and experimental data allows one to regard the model as a good tool for design purposes.