Gas transport properties of two sets of polynorbornenes bearing carbocyclic substituents of different nature (cyclohexyl, norbornyl, phenyl groups, and framed oligocyclic moieties) were systematically studied. The influence of side chain carbocyclic substituents on gas permeability and separation selectivity for CO2-containing gas pairs and gaseous hydrocarbons was evaluated. It was found that the presence of carbocyclic moieties in side chains of polynorbornenes promotes the increase in gas permeability similarly to that of SiMe3 groups, with this effect being enhanced by the increase in the number of cycles in the substituents. As a result, P(CO2) of the metathesis polymer with pentacene-based substituents is equal to 1200 Barrer. Studied polynorbornenes with carbocyclic substituents displayed promising gas separation selectivities: CO2/N2 separation selectivity up to 41 (above the 2008 upper bound in the Robeson diagram) and solubility-controlled hydrocarbon separation selectivity up to 16 for the n-butane/methane gas pair. For the polymer with pentacene-based substituents, the separation of the mixture of hydrocarbons and aging were studied. The studies revealed that the mixed gas C4/C1 separation selectivity of this polymer reaches 4, and a two-time reduction of permeability occurs in 8.5 months. Therefore, the incorporation of carbocyclic groups in the side chains of polynorbornenes can be considered as an efficient strategy for the design of polymeric gas separation membrane materials.