Gas separation membranes are made from aromatic polyimides, polyesters and polyamides in which the repeating unit of the main polymer chainA. has at least one rigid divalent subunit, the two main chain single bonds extending from which are not colinear,B. is sterically unable to rotate 360.degree. around at least one of these bonds, andC. has 50% or more of its main chain atoms as members of aromatic rings.