Mixed conducting dense ceramic gas separation membranes can be used in air separation for oxy-fuel and precombustion processes in CO2 capture schemes for emission-free power plants and chemical industries. Such membranes operate at high temperatures, and the energy penalty associated with heating the membranes with external electrical heaters or burners via the feed or sweep gas can be significantly reduced by adopting direct ohmic heating of the membrane. We demonstrate that tubular asymmetric gas separation membranes of La2NiO4+delta and La0.87Sr0.13CrO3-delta can be heated to temperatures in excess of 800 degrees C by passing current through them, and that such ohmically heated tubular membranes can be operated in an oxygen potential gradient to selectively separate oxygen from a feed gas mixture. We highlight the associated challenges with heat transport and thermal gradients and undertake numerical simulations to investigate the effect of materials properties on heating power and heat distribution in the tubes.