The present application relates to new compounds in the family of N-acylamino-amides having formula (I), compositions, in particular cosmetic compositions comprising them, and their use to treat the signs of aging of skin of the body or face, whether chronobiological or photo-induced, and in particular aging generated by reduced skin elasticity. in which p=1, 2 or 3 R independently denotes a cyano (—CN), hydroxy (—OH), CO2R′ group in which R′ denotes a hydrogen atom or linear or branched C1-C6 alkyl group, R1 denotes a hydrogen atom or a linear or branched C1-C6 alkyl group, and also the salts and/or isomers and/or solvates thereof.