A process for preparing copolymers, preferably degradable copolymers, said process comprising at least one step of radical ring-opening polymerization of at least one cyclic monomer with at least one monomer comprising an ethylenic unsaturation, in the presence of a radical polymerization initiator, said process being characterized in that: (i) the cyclic monomer is chosen from thionolactones and thionocarbonates of following formula: wherein: - X is an oxygen atom or a -CH 2 - group; - Y is chosen from -CH 2 -, -CH 2 -O-CH 2 -, -O-CH 2 -CH 2, -CH 2 -CH 2 -O-CH 2 -CH 2 and CH 2 -O-CH 2 -CH 2 groups; - n is an integer greater than or equal to 1; it being understood that: - when Y represents a -CH 2 - group, then n is greater than or equal to 4, - when X represents an oxygen atom, then Y is other than an -O-CH 2 -CH 2 - group; and - when X represents a -CH 2 - group, and when Y represents an -O-CH 2 -CH 2 - group, then the oxygen atom of the Y group is connected to X; and in that (ii) the monomer comprising an ethylenic unsaturation is chosen from the monomers of formula below: wherein: - R 1, R 2 and R 3 are identical and represent a hydrogen atom, - R 4 represents a hydrogen atom, an alkyl radical, or a group chosen from imidazole, alkylimidazolium, carbazole, -OC R 5 groups, or a group of formula below: - R 5 represents an alkyl, haloalkyl, trifluoroalkyl, aryl or arylalkyl radical, - the asterisk (*) represents the anchoring point of the group of formula to the carbon atom of the compound of formula, - R 6 and R 7, which are identical or different, represent a hydrogen atom, an alkyl, cycloalkyl, arylalkyl, aryl, glycidyl radical, or else R 6 and R 7, together with the nitrogen and carbon atoms of the group of formula to which they are bonded, form a heterocycle comprising from 4 to 7 carbon atoms. (i) the cyclic monomer is chosen from thionolactones and thionocarbonates of following formula: wherein: - X is an oxygen atom or a -CH 2 - group; - Y is chosen from -CH 2 -, -CH 2 -O-CH 2 -, -O-CH 2 -CH 2, -CH 2 -CH 2 -O-CH 2 -CH 2 and CH 2 -O-CH 2 -CH 2 groups; - n is an integer greater than or equal to 1; it being understood that: - when Y represents a -CH 2 - group, then n is greater than or equal to 4, - when X represents an oxygen atom, then Y is other than an -O-CH 2 -CH 2 - group; and - when X represents a -CH 2 - group, and when Y represents an -O-CH 2 -CH 2 - group, then the oxygen atom of the Y group is connected to X; and in that - X is an oxygen atom or a -CH 2 - group; - Y is chosen from -CH 2 -, -CH 2 -O-CH 2 -, -O-CH 2 -CH 2, -CH 2 -CH 2 -O-CH 2 -CH 2 and CH 2 -O-CH 2 -CH 2 groups; - n is an integer greater than or equal to 1; - when Y represents a -CH 2 - group, then n is greater than or equal to 4, - when X represents an oxygen atom, then Y is other than an -O-CH 2 -CH 2 - group; and - when X represents a -CH 2 - group, and when Y represents an -O-CH 2 -CH 2 - group, then the oxygen atom of the Y group is connected to X; and in that (ii) the monomer comprising an ethylenic unsaturation is chosen from the monomers of formula below: wherein: - R 1, R 2 and R 3 are identical and represent a hydrogen atom, - R 4 represents a hydrogen atom, an alkyl radical, or a group chosen from imidazole, alkylimidazolium, carbazole, -OC R 5 groups, or a group of formula below: - R 5 represents an alkyl, haloalkyl, trifluoroalkyl, aryl or arylalkyl radical, - the asterisk (*) represents the anchoring point of the group of formula to the carbon atom of the compound of formula, - R 6 and R 7, which are identical or different, represent a hydrogen atom, an alkyl, cycloalkyl, arylalkyl, aryl, glycidyl radical, or else R 6 and R 7, together with the nitrogen and carbon atoms of the group of formula to which they are bonded, form a heterocycle comprising from 4 to 7 carbon atoms. - R 1, R 2 and R 3 are identical and represent a hydrogen atom, - R 4 represents a hydrogen atom, an alkyl radical, or a group chosen from imidazole, alkylimidazolium, carbazole, -OC R 5 groups, or a group of formula below: - R 5 represents an alkyl, haloalkyl, trifluoroalkyl, aryl or arylalkyl radical, - the asterisk (*) represents the anchoring point of the group of formula to the carbon atom of the compound of formula, - R 6 and R 7, which are identical or different, represent a hydrogen atom, an alkyl, cycloalkyl, arylalkyl, aryl, glycidyl radical, or else R 6 and R 7, together with the nitrogen and carbon atoms of the group of formula to which they are bonded, form a heterocycle comprising from 4 to 7 carbon atoms.