Norbornene-ethylene copolymers with relatively high norbornene content, synthesised using different metallocene catalysts, were studied by Microhardness methods and Positron Annihilation Lifetime Spectroscopy. It has been established that plastic and elastic properties as well as free volume of the investigated materials do not depend linearly on the norbornene content since the different molecular structures, as a result of the various catalytic systems used, have also an important influence on those parameters. Vickers microhardness and plastic properties of the samples investigated are not sensitive to the quantity of ethylene blocks and are influenced predominantly by micromechanical properties of polymer chains. Vickers microhardness is not sensitive either to dimensions and quantity of the pores or to the free volume. On the other hand, long ethylene sequences are related to total microhardness, i.e., during penetration they contribute to the elastic deformation. The sizes, distribution and quantity of the nanopores have been determined and explained in relation to the structure of the norbornene-ethylene copolymers.