Cosmetic composition, more particularly styling composition, comprising, in a cosmetically acceptable vehicle, a) at least one copolymer A formed from at least one monomer A1 selected from acrylic acid, methacrylic acid, acrylic acid alkyl esters and methacrylic acid alkyl esters, and at least one amphoteric monomer A2 selected from (meth)acryloylalkylbetaines of the formula (A2-I) and(meth)acryloylalkylamine oxides of the formula (A2-II), where in formula (A2-I) and in formula (A2-II), R