A cosmetic composition has an association of at least three of the following substances with anti-free radical activity, selected from: 1) ebselen； or idebenone； or an association of the two； and 2) at least one substance with anti-free radical activity, or at least two substances with anti-free radical activity for obtaining said association of at least three substances with anti-free radical activity, said substance(s) being selected from: a) a substance of chemical formula (I) below: in which: R=a linear or branched, saturated or unsaturated C1-C16 hydrocarbon chain； and R1, R2 and R3 are identical or different and are a hydrogen atom or a methyl or methoxy radical, and its esters； b) an extract of Edelweiss； c) an extract of Emblica； and d) N-acetylcysteine. The anti-free radical activity is greatly improved.
