Process for producing carbon membranes

The use of solutions of ethylenically unsaturated polyesters for production of carbon membranes suitable for gas separation, and a process for producing carbon membranes suitable for gas separation, comprising the steps of a) coating a porous substrate with a solution of ethylenically unsaturated polyester, b) drying the polyester coating on the porous substrate by removing the solvent, and c) pyrolyzing the polyester coating on the porous substrate to form the carbon membrane suitable for gas separation, it being possible to conduct any of steps a) to c) or the sequence of steps a) to c) more than once.