Polynorbornenes with different contents of cis units were prepared with the catalysts of metathesis ring-opening polymerization, which show different stereoselectivity (Re2O7, RuCl3, WCl6). It was shown that polynorbornene synthesized with WCl6, which contains nearly equal amounts of cia and trans units, is characterized by the highest diffusion coefficients for gases. The polymers, that predominantly consist of cia units in the backbone chain show higher gas permeabilities P, higher diffusion D and solubility coefficients S for gases. The separation factors alpha(ij) = P-i/P-j are maximal for the polymers with trans configuration of the chains, which exhibit minimal P-i values.