Process for the preparation of random copolymers of mono-olefins or of mono-olefins and unconjugated dienes with lactams with substitution on the nitrogen atom by an unsaturated radical

A process for the preparation of substantially linear amorphous, random copolymers of mono-olefins, or mono-olefins and unconjugated dienes, with unsaturated lactams of the general formula ##EQU2## where R.sub.1 is a monovalent alkenyl radical containing 2 to 8 carbon atoms, R.sub.2 and R.sub.3, which are identical or different, represent hydrogen or a monovalent hydrocarbon radical, free of ethylenic unsaturation and containing 1 to 8 carbon atoms, X represents oxygen or sulphur, and n is an integer of from 3 to 14 representing the number of repeating units ##EQU3## in the lactam ring so that the number of carbon atoms in the ring is equal to (n = 1) comprising contacting at least 2 mono-olefins containing from 2 to 20 carbon atoms in their molecules or at least 2 such mono-olefins and an unconjugated diene, in an inert liquid medium at a temperature of between -80.degree.C and +150.degree.C, with at least one of said unsaturated lactams, in the form of a complex formed with a Lewis acid, in at least stoichiometric amounts, in the presence of a catalytically effective amount of a catalyst system formed by the combination of an organometallic compound of at least one metal in columns I, II, or III of the periodic table of elements with a compound of a transition metal in columns IV to VIII of the 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 said copolymer.