A method for separating aromatic hydrocarbons from feed streams comprising mixtures of aromatic hydrocarbons and non-aromatic hydrocarbons, said method comprising contacting the feed stream with one side of a membrane made from a multi-block polymer material comprising a first prepolymer made by combining (A) a diamine with (B) a dianhydride or its corresponding tetraacid or diacid-diester in an A/B mole ratio ranging from about 2.0 to 1.05, to produce an amide acid prepolymer which is subsequently chain extended with a second compatible prepolymer selected from the group consisting of (A) a dianhydride or its corresponding tetraacid or diacid-diester combined with a monomer selected from the group consisting of (B) epoxy, diisocyanate and polyester in an A/B mole ratio ranging from about 2.0 to 1.05, and mixtures thereof, said separation being conducted under pervaporation or perstraction conditions, whereby the aromatic hydrocarbon components of the feed stream selectively permeate through the membrane.