Process for treating keratin fibres using a compound derived from the condensation of poly(thi)ol and of acetoacetate and a crosslinking agent

A process for treating keratin fibres in one or more steps by applying to said fibres:

• i) one or more compounds of formula (I), the optical isomers thereof, the geometrical isomers thereof, the salts thereof, the solvates thereof, the hydrates:
• in which formula (I):
• R1 represents a linear or branched, saturated or unsaturated, conjugated or non-conjugated, acyclic or cyclic, aromatic or non-aromatic C2 to C14 polyvalent hydrocarbon-based radical,
• R1 also being:
• a) optionally substituted with one or more hydroxyl OH or dialkylamino —N(R)2 groups with R representing a (C1-C4)alkyl group, carboxyl —C(O)—OH, a vinyl group, and
• b) optionally interrupted with one or more heteroatoms or groups chosen from O, S, carbonyl —C(O)—, amine —N(R′), or combinations thereof, in which R′ represents a hydrogen atom, a linear or branched alkyl group containing from 1 to 4 carbon atoms optionally substituted with at least one hydroxyl group (OH), or optionally substituted with —X—C(O)—C(Ra)(Rb)—C(O)—R2;
• R2 represents a linear or branched, saturated or unsaturated C1-C6 monovalent hydrocarbon-based radical;
• Ra and Rb, which may be identical or different, represent a hydrogen atom or a (C1-C4)alkyl group;
• X is a heteroatom or group chosen from O, S, N(R′) or —S—CH2—C(O)—O—, —O—C(O)—CH2—S—, —O—C(O)—N(R′)—, —N(R′)—C(O)—O— or —N(R′)—C(O)—N(R′)—;
• n denotes an integer ranging from 2 to 10, particularly ranging from 3 to 8;
• and
• ii) at least one crosslinking agent;
• and
• iii) optionally at least one cosmetic active agent.