This is the second communication of a series dealing with an experimental and modelling study on propane catalytic combustion in a membrane reactor with separate feed of reactants. In paper I the behaviour of the reactor in the absence of trans-membrane pressure gradients was presented and discussed. Attention is here focused on the reactor behaviour when pressure differences are applied over the membrane, resulting in a convective flow through the membrane itself. By these means, a major conversion enhancement (up to more than 300%) is achievable compared to the case in which only diffusive mass transfer controls the reactor performance. However, above certain pressure differences (> 1 bar), this is obtained at the price of noticeable slip of unconverted reactants across the membrane. The experimental results are in good agreement with the predictions of an isothermal model based on the numerical solution of differential mass balances across the membrane, employing a Stefan-Maxwell expression for diffusive fluxes and a d'Arcy law for convective ones.