NOVELTY - An aromatic poly(ether sulfone imide) polymer membrane or a crosslinked aromatic poly(ether sulfone imide) polymer membrane is provided. A mixture of gases/liquids is contacted to one side of aromatic poly(ether sulfone imide) polymer membrane or cross-linked aromatic poly(ether sulfone imide) polymer membrane, to permeate gas/liquid through the membrane. A permeate gas/liquid composition comprising a portion of permeated gas/liquid is removed from opposite side the membrane. The aromatic poly(ether sulfone imide) polymer membrane comprises a repeating unit (I) or (II).    USE - Separation of gas or liquid e.g. gasoline, naphtha and diesel fuels (from water or sulfur compounds) from mixture of gases/liquids e.g. mixture of volatile organic compounds in atmospheric gas, mixture of helium, carbon dioxide or hydrogen sulfide in natural gas, and mixture of hydrogen, nitrogen, methane and argon in ammonia purge gas streams or hydrogen in stream from refinery, mixture of olefins and paraffins, mixture of xylenes, mixture of (iso)paraffins and mixture of liquids in natural gas (all claimed).    ADVANTAGE - The method enables separation of gas/liquid from mixture of gases/liquids with high purity, using economical membrane having high selectivity and permeability.    DETAILED DESCRIPTION - An aromatic poly(ether sulfone imide) polymer membrane or a crosslinked aromatic poly(ether sulfone imide) polymer membrane is provided. A mixture of gases or a mixture of liquids is contacted to one side of the aromatic poly(ether sulfone imide) polymer membrane or the cross-linked aromatic poly(ether sulfone imide) polymer membrane, to permeate at least one gas or liquid(s) through the membrane. A permeate gas composition or permeate liquid composition comprising a portion of permeated gas or liquid is removed from opposite side of aromatic poly(ether sulfone imide) polymer membrane or crosslinked aromatic poly(ether sulfone imide) polymer membrane. The aromatic poly(ether sulfone imide) polymer membrane comprises a repeating unit of formula (I) or (II).    X1=group chosen from groups of formulae (i)-(vii);    Y1=group chosen from groups of formulae (viii)-(xvi);    Y2=group of formula (xvii) or (xviii);    n,m,o,p=2-500;and    or (n+o)/(m+p)=1:10-10:1.