Adhesive composition comprising: - a composition A consisting of: - at least one cyclocarbonate-terminated polyurethane prepolymer; - optionally at least one crosslinking catalyst, - optionally at least one mineral filler, - optionally at least one adhesion promoter selected from the group consisting of silanes, aminosilanes or acryloyl silanes, - optionally at least one additive selected from the group consisting of ultraviolet stabilizers or antioxidants, pigments and dyes, and at least one solvent selected from organic and alcoholic solvents and - a composition B consisting of: - at least one diamine B1 comprising only two -CH 2 -NH 2 groups, and at least one polyamine B2 comprising at least three -CH 2 -NH 2 groups, present in a diamine B1:polyamine B2 weight ratio of from 30/70 to 70/30, - optionally at least one crosslinking catalyst, - optionally at least one mineral filler, - optionally at least one adhesion promoter selected from the group consisting of silanes, aminosilanes or acryloyl silanes, - optionally at least one additive selected from the group consisting of ultraviolet stabilizers or antioxidants, pigments and dyes, in which the molar ratio of the number of primary amine functions to the number of cyclocarbonate functions ranges from 0.8 to 1.2; the adhesive composition comprising up to 2% by weight, relative to the total weight of the adhesive composition, of said at least one additive, if present; and said cyclocarbonate-terminated polyurethane prepolymer being prepared by a process comprising the following steps: E1) the preparation of an NCO-terminated polyurethane prepolymer by a polyaddition reaction: i) of at least one polyisocyanate selected from diisocyanates and triisocyanates, ii) with at least one polyol selected from polyether polyols and polyester polyols, and mixtures thereof; followed by E2) the reaction of the product formed in the first step E1) with at least one glycerol cyclocarbonate in an amount such that all of the NCO groups present in the reaction medium at the end of step E1) react in the presence of the glycerol carbonate. - a composition A consisting of: - at least one cyclocarbonate-terminated polyurethane prepolymer; - optionally at least one crosslinking catalyst, - optionally at least one mineral filler, - optionally at least one adhesion promoter selected from the group consisting of silanes, aminosilanes or acryloyl silanes, - optionally at least one additive selected from the group consisting of ultraviolet stabilizers or antioxidants, pigments and dyes, and at least one solvent selected from organic and alcoholic solvents and - at least one cyclocarbonate-terminated polyurethane prepolymer; - optionally at least one crosslinking catalyst, - optionally at least one mineral filler, - optionally at least one adhesion promoter selected from the group consisting of silanes, aminosilanes or acryloyl silanes, - optionally at least one additive selected from the group consisting of ultraviolet stabilizers or antioxidants, pigments and dyes, and - a composition B consisting of: - at least one diamine B1 comprising only two -CH 2 -NH 2 groups, and at least one polyamine B2 comprising at least three -CH 2 -NH 2 groups, present in a diamine B1:polyamine B2 weight ratio of from 30/70 to 70/30, - optionally at least one crosslinking catalyst, - optionally at least one mineral filler, - optionally at least one adhesion promoter selected from the group consisting of silanes, aminosilanes or acryloyl silanes, - optionally at least one additive selected from the group consisting of ultraviolet stabilizers or antioxidants, pigments and dyes, - at least one diamine B1 comprising only two -CH 2 -NH 2 groups, and at least one polyamine B2 comprising at least three -CH 2 -NH 2 groups, present in a diamine B1:polyamine B2 weight ratio of from 30/70 to 70/30, - optionally at least one crosslinking catalyst, - optionally at least one mineral filler, - optionally at least one adhesion promoter selected from the group consisting of silanes, aminosilanes or acryloyl silanes, - optionally at least one additive selected from the group consisting of ultraviolet stabilizers or antioxidants, pigments and dyes, E1) the preparation of an NCO-terminated polyurethane prepolymer by a polyaddition reaction: i) of at least one polyisocyanate selected from diisocyanates and triisocyanates, ii) with at least one polyol selected from polyether polyols and polyester polyols, and mixtures thereof; followed by i) of at least one polyisocyanate selected from diisocyanates and triisocyanates, ii) with at least one polyol selected from polyether polyols and polyester polyols, and mixtures thereof; followed by E2) the reaction of the product formed in the first step E1) with at least one glycerol cyclocarbonate in an amount such that all of the NCO groups present in the reaction medium at the end of step E1) react in the presence of the glycerol carbonate.