Improved composite semipermeable membranes comprising microporous carbonaceous adsorptive material supported by a porous substrate are disclosed for use in separating multicomponent gas mixtures in which certain components in the mixture adsorb within the pores of the adsorptive material and diffuse by surface flow through the membrane to yield a permeate stream enriched in these components. Methods for making the improved composite membranes are described including one or more oxidation steps which increase the membrane permeability and selectivity.