Cosmetic composition comprising a derivative imido-peroxycarboxylic acid and a bis-akyl sulfosuccinate

The invention relates to a composition comprising, in a physiologically acceptable aqueous medium, an imido-peroxycarboxylic acid compound of formula (I): wherein: - A represents an optionally substituted benzene ring - R represents a hydrogen atom, -OH, a (C -C) alkyl, -COOH, -COOR, wherein R represents a (C -C) alkyl, and - n is an integer ranging from 1 to 12, and salts thereof ; and a sulfosuccinate compound bis-akyl of formula (II): wherein: R and R, identical or different, denote a linear alkyl radical of C -C linear or branched C -C; M represents a cation selected from sodium, potassium, lithium or ammonium. Application to the treatment of oily skin.