Process for the preparation of a hydrocarbon polymer comprising two end groups having 2-oxo-1,3-dioxolan-4-yl final parts by ring opening metathesis in the presence of a metathesis catalyst, of a chain transfer agent comprising a carbonate ring and of a compound of formula comprising at least one C6-C16 ring having a carbon-carbon double bond.Hydrocarbon polymer capable of being obtained by this process.Process for the preparation of polyurethanes by reaction of this polymer and of a compound comprising at least one amine group, and polyurethanes thus obtained.