Poly(l-trimethylsilyl-l-propyne) [PTMSP], a high-free-volume glassy polymer, has the highest gas permeability of any known synthetic polymer. In contrast to conventional, low-free-volume, glassy polymers, PTMSP is more permeable to large, condensable organic vapors than to permanent gases. The organic-vapor/permanent-gas selectivity of PTMSP based on pure gas measurements is low. In organic-vapor/permanent-gas mixtures, however, the selectivity of PTMSP is much higher because the permeability of the permanent gas is reduced dramatically by the presence of the organic vapor, For example, in n-butane/methane mixtures, as little as 2 mol% n-butane (relative n-butane pressure 0.16) lowers the methane permeability 10-fold from the pure methane permeability. The result is that PTMSP shows a mixed-gas n-butane/methane selectivity of 30. This selectivity is the highest ever observed for this mixture and is completely unexpected for a glassy polymer. In addition, the gas mixture n-butane permeability of PTMSP is considerably higher than that of any known polymer, including polydimethylsiloxane, the most vapor-permeable rubber known. PTMSP also shows high mixed-gas selectivities and vapor permeabilities for the separation of chlorofluorocarbons from nitrogen. The unusual vapor permeation properties of PTMSP result from its very high free volume - more than 20% of the total volume of the material. The free volume elements appear to be connected, forming the equivalent of a finely microporous material. The large amount of condensable organic vapor sorbed into this finely porous structure causes partial blocking of the small free-volume elements, reducing the permeabilities of the noncondensable permanent gases from their pure gas values.