When polymeric membranes are employed to remove selectively one component from a gaseous mixture, there is generally a trade-off between selectivity and permeability. Data are presented for two polymers of intrinsic microporosity, PIM-1 and PIM-7, which show a significant advance across the previous upper bound of performance for commercially important gas pairs, including O-2/N-2 and CO2/CH4. The exceptional properties of PIMs arise from their rigid but contorted molecular structures, which frustrate packing and so create free volume, coupled with chemical functionality giving strong intermolecular interactions. (c) 2005 Elsevier B.V. All rights reserved.