A process for the preparation of substantially linear, amorphous, random copolymers of mono-olefins, or mono-olefins and unconjugated dienes, with a member selected from the group consisting of N-vinylimidazole, N-vinylimidazoline, ring substituted N-vinyl-imidazoles and ring substituted N-vinylimidazolines wherein the substituents are hydrocarbon radicals and amino-hydrocarbon radicals, comprising contacting at least two mono-olefins containing from 2 to 20 carbon atoms in their molecule or at least two such mono-olefins and said unconjugated diene in a liquid medium at a temperature of between -80.degree. to 150.degree.C with at least one of the said members in the form of a complex with a Lewis acid, in the presence of the catalyst system formed by the combination of an organometallic compound of at least one metal in column I, II or III of the periodic table of elements with a compound of a transition metal in columns IV to VIII of said periodic table at a ratio of the number of atoms of the first metal to the number of atoms of the second metal of between 1 and 50, to obtain the desired copolymer.