Cosmetic or dermatological composition comprising, in a cosmetically or dermatologically acceptable medium, a polymer comprising: (a) a polymer backbone that may be obtained by reacting: - from 10% to 60% by weight, relative to the total weight of the said backbone, of at least one polyol comprising 3 to 6 hydroxyl groups; - from 0.1% to 80% by weight, relative to the total weight of the said backbone, of a mixture of aromatic monocarboxylic acid containing 6 to 32 carbon atoms and of non aromatic monocarboxylic acid containing 6 to 32 carbon atoms; - from 5% to 60% by weight, relative to the total weight of the said backbone, of at least one polycarboxylic acid comprising at least two carboxylic groups COOH, and/or a cyclic anhydride of such a polycarboxylic acid; and - (b) at least one junction group linked to the said polymer backbone and capable of establishing H bonds with one or more partner junction groups, each pairing of a junction group involving at least three H (hydrogen) bonds, said backbone being linked to the junction group by at least one urethane function, the junction group bearing isocyanate groups being of formula OCN-A-NCO, the divalent radical A having the structure: in which: - R1 and R3, which may be identical or different, represent a divalent carbon-based radical chosen from (i) a linear or branched C 1 -C 30 alkyl group, (ii) a C 4 -C 12 cycloalkyl group and (iii) a C 4 -C 12 aryl group; optionally comprising 1 to 8 heteroatoms chosen from O, N, S, F, Si and P; and/or optionally substituted with an ester or amide function or with a C 1 -C 12 alkyl radical; or a mixture of these groups; - R2 represents H, halogen (Br, Cl or F) or a linear, branched or cyclic, saturated or unsaturated, optionally aromatic C 1 -C 32 monovalent hydrocarbon-based group, which may contain one or more heteroatoms chosen from O, S, N, P and F, or of formula B-NCO, the monovalent radical B having the formula: in which: - the radical R1 represents a divalent carbon-based group chosen from (i) a linear or branched C 1 -C 30 alkyl group, (ii) a C 4 -C 12 cycloalkyl group and (iii) a C 4 -C 12 aryl group; optionally comprising 1 to 8 heteroatoms chosen from O, N, S, F, Si and P; and/or optionally substituted with an ester or amide function or with a C 1 -C 12 alkyl radical; or a mixture of these groups; - the radicals R2 and R3, which may be identical or different, represent a hydrogen atom or a linear, branched or cyclic, saturated or unsaturated C 1 -C 32 carbon-based, especially hydrocarbon-based (alkyl), radical, which may comprise one or more heteroatoms chosen from O, N, S, F, Si and P. (a) a polymer backbone that may be obtained by reacting: - from 10% to 60% by weight, relative to the total weight of the said backbone, of at least one polyol comprising 3 to 6 hydroxyl groups; - from 0.1% to 80% by weight, relative to the total weight of the said backbone, of a mixture of aromatic monocarboxylic acid containing 6 to 32 carbon atoms and of non aromatic monocarboxylic acid containing 6 to 32 carbon atoms; - from 5% to 60% by weight, relative to the total weight of the said backbone, of at least one polycarboxylic acid comprising at least two carboxylic groups COOH, and/or a cyclic anhydride of such a polycarboxylic acid; and - (b) at least one junction group linked to the said polymer backbone and capable of establishing H bonds with one or more partner junction groups, each pairing of a junction group involving at least three H (hydrogen) bonds, - from 10% to 60% by weight, relative to the total weight of the said backbone, of at least one polyol comprising 3 to 6 hydroxyl groups; - from 0.1% to 80% by weight, relative to the total weight of the said backbone, of a mixture of aromatic monocarboxylic acid containing 6 to 32 carbon atoms and of non aromatic monocarboxylic acid containing 6 to 32 carbon atoms; - from 5% to 60% by weight, relative to the total weight of the said backbone, of at least one polycarboxylic acid comprising at least two carboxylic groups COOH, and/or a cyclic anhydride of such a polycarboxylic acid; and - (b) at least one junction group linked to the said polymer backbone and capable of establishing H bonds with one or more partner junction groups, each pairing of a junction group involving at least three H (hydrogen) bonds, - R1 and R3, which may be identical or different, represent a divalent carbon-based radical chosen from (i) a linear or branched C 1 -C 30 alkyl group, (ii) a C 4 -C 12 cycloalkyl group and (iii) a C 4 -C 12 aryl group; optionally comprising 1 to 8 heteroatoms chosen from O, N, S, F, Si and P; and/or optionally substituted with an ester or amide function or with a C 1 -C 12 alkyl radical; or a mixture of these groups; - R2 represents H, halogen (Br, Cl or F) or a linear, branched or cyclic, saturated or unsaturated, optionally aromatic C 1 -C 32 monovalent hydrocarbon-based group, which may contain one or more heteroatoms chosen from O, S, N, P and F, - the radical R1 represents a divalent carbon-based group chosen from (i) a linear or branched C 1 -C 30 alkyl group, (ii) a C 4 -C 12 cycloalkyl group and (iii) a C 4 -C 12 aryl group; optionally comprising 1 to 8 heteroatoms chosen from O, N, S, F, Si and P; and/or optionally substituted with an ester or amide function or with a C 1 -C 12 alkyl radical; or a mixture of these groups; - the radicals R2 and R3, which may be identical or different, represent a hydrogen atom or a linear, branched or cyclic, saturated or unsaturated C 1 -C 32 carbon-based, especially hydrocarbon-based (alkyl), radical, which may comprise one or more heteroatoms chosen from O, N, S, F, Si and P.