Process for the preparation of at least one hydrocarbon polymer comprising two end groups having 2-oxo-1,3-dioxolan-4-yl final parts, said process comprising at least one stage of ring opening metathesis polymerization in the presence: - of at least one metathesis catalyst, preferably a ruthenium-comprising catalyst, more preferably still a Grubbs' catalyst; - of at least one chain transfer agent compound of formula: - the Z group being composed of at least one alkylene group optionally connected to a divalent carboxyl or oxy group, the Z group comprising from 1 to 19 carbon atoms and q being an integer equal to 0 or 1; and - of at least one compound chosen from compounds comprising at least one hydrocarbon ring and generally from 6 to 16, preferably from 6 to 12, carbon atoms per ring, said ring comprising at least one carbon-carbon double bond, and the substituted derivatives of this compound, said compound being of formula: in which: - each carbon-carbon bond of the chain denoted is a double bond or a single bond, in accordance with the valency rules of organic chemistry; - the R 1 and R 6 groups are either both hydrogen or each different from hydrogen and bonded to one another as members of one and the same ring or heterocycle which is saturated or unsaturated (i.e., comprising at least one carbon-carbon double bond, including aromatics); - the R 2, R 3, R 4 and R 5 groups are each, independently or not of the other groups, a hydrogen, a halo group, an alkoxycarbonyl group or an alkyl group, it being possible for the R 2 to R 5 groups to be bonded to one another as members of one and the same saturated or unsaturated ring or heterocycle; - m and p are integers each within a range extending from 0 to 5, the sum m + p being itself within a range from 0 to 6; said stage being carried out for a period of time strictly of greater than 3 h when the compound of formula is 4-vinyl-1,3-dioxolan-2-one and for a period of time of greater than or equal to 2 h in all the other cases. - of at least one metathesis catalyst, preferably a ruthenium-comprising catalyst, more preferably still a Grubbs' catalyst; - of at least one chain transfer agent compound of formula: - the Z group being composed of at least one alkylene group optionally connected to a divalent carboxyl or oxy group, the Z group comprising from 1 to 19 carbon atoms and q being an integer equal to 0 or 1; and - of at least one compound chosen from compounds comprising at least one hydrocarbon ring and generally from 6 to 16, preferably from 6 to 12, carbon atoms per ring, said ring comprising at least one carbon-carbon double bond, and the substituted derivatives of this compound, said compound being of formula: in which: - each carbon-carbon bond of the chain denoted is a double bond or a single bond, in accordance with the valency rules of organic chemistry; - the R 1 and R 6 groups are either both hydrogen or each different from hydrogen and bonded to one another as members of one and the same ring or heterocycle which is saturated or unsaturated (i.e., comprising at least one carbon-carbon double bond, including aromatics); - the R 2, R 3, R 4 and R 5 groups are each, independently or not of the other groups, a hydrogen, a halo group, an alkoxycarbonyl group or an alkyl group, it being possible for the R 2 to R 5 groups to be bonded to one another as members of one and the same saturated or unsaturated ring or heterocycle; - m and p are integers each within a range extending from 0 to 5, the sum m + p being itself within a range from 0 to 6;