The invention relates to the use of compounds of formula (I) R—N1-spermidine, i.e. 1.4-butanediamine,N-(3-aminopropyl)-N1—R, (I) H2N —(CH2)3—N1(R)—(CH2)4—NH2, as such or in the form of pharmaceutically acceptable derivatives, as active principle in a cosmetic or pharmaceutical composition for resisting the effects of skin ageing through an anti-inflammatory action, by topical administration. Such compounds also have an antioxidant activity against oxygen free radicals (ROS) comparable with that of α-tocopherol.