In a high‐temperature catalytic membrane reactor, a plug‐flow reactor is combined with a gas‐separative membrane. By selectively removing one of the reaction products, the reaction mixture is prevented from reaching equilibrium, and a higher conversion can be obtained. This concept is only valid for reactions that are limited by the thermodynamic equilibrium, such as the direct dehydrogenation of propane to propene. A tubular H2‐selective silica membrane was characterized [αH2/C3H8 = 70–90 at 500°C] and used as the gas‐separative membrane. The membrane reactor was filled with a chromia/alumina catalyst. The kinetics of the catalyst was studied. At 500°C the deactivation of the catalyst is slow, and the propene yield is almost constant for at least 10 h of operation. Under well‐chosen process conditions, the propene yield is at least twice as high as the value obtained at thermodynamic equilibrium in a conventional reactor.