A process for producing oxacarbonylated polymers, reacting at least a monomer comprising at least one cyclic oxacarbonyl function, and an initiator and polymerizing or copolymerization said monomer in bulk or in solution to produce oxacarbonylated polymers, wherein the initiator is chosen from the bicyclic guanidine compounds corresponding to formula (I) or (II)
- and from the bicyclic guanidine compounds corresponding to formula (I) in which at least any one of positions 2, 3, 4, 8, 9 and 10 is substituted and from the bicyclic biguanidine compounds corresponding to formula (II) in which at least any one of positions 2, 3, 7 and 8 is substituted, said position at least being substituted with at least one radical chosen from alkyl groups having from 1 to 6 carbon atoms, cycloalkyl groups having from 5 to 7 carbon atoms and the hydrocarbon-based chains of polystyrene.