A cosmetic composition (C1) comprises at least one electrophilic monomer, and at least one non-reducing organic acid (A1) containing 1 to 12 carbon atom, in a cosmetically acceptable anhydrous medium selected from at least one organic oils, silicones, mineral oils, plant oils, waxes, 5-10C alkanes, acetone, methyl ethyl ketone, 1-20C acid esters of 1-8C alcohols, dimethoxyethane, diethoxyethane, or 10-30C fatty alcohols, acids, amides, or esters. Independent claims are included for the following: (1) method of cosmetically treating hair involving: (M1) applying (C1); or (M2) applying (A1) and electrophilic monomer (A2) separately to the hair; and (2) a multi-compartment kit comprising a first composition comprising at least one (A2) and optionally comprising at least one polymerization inhibitor; and a second composition comprising at least one (A1) in a cosmetically acceptable anhydrous medium.La présente invention concerne une composition comprenant, dans un milieu cosmétiquement acceptable anhydre, au moins un monomère électrophile et au moins un acide organique non-réducteur comportant de 1 à 12 atomes de carbone, et son utilisation pour le traitement cosmétique des cheveux.Elle concerne aussi un procédé de traitement cosmétique des cheveux mettant en oeuvre ladite composition.