Metathesis homo- and copolymerization of bifunctional monomers bearing two norbornene moieties was studied. The monomers were synthesized from cis-5-norbornene-exo-2,3-dicarboxylic anhydride and various diamines (hexamethylenediamine, decamethylenediamine, 1R,3S-isophoronediamine). The metathesis homopolymerization of these bis(nadimides) in the presence of the second-generation Grubbs catalyst afforded glassy cross-linked polymers in more than 90% yields. The metathesis copolymerization of the bis(nadimides) and a monofunctional norbornene derivative containing the β-pinene fragment also resulted in insoluble cross-linked polymers in nearly quantitative yields. The structures and purity of the synthesized polymers were confirmed via IR spectroscopy and CP/MAS NMR spectroscopy. Conditions for the fabrication of mechanically strong solution-cast thin films based on copolymers synthesized from the comonomers mentioned above were determined by varying the content of the cross-linking agent. It was shown that the films made in this way are stable in a range of organic solvents and could be useful as semipermeable or membrane materials for use in liquid organic media. The permeability of the polymer films in question to 1-phenylethanol and mandelic acid was studied. The results obtained are discussed along with the data from the DSC, TGA, and powder X-ray diffraction studies of the properties of the synthesized metathesis homo- and copolymers.