Abstract: The present invention relates to a cosmetic composition comprising, in a physiologically acceptable medium, at least one statistical copolymer with a linear main chain of ethylenic nature, in which the said copolymer has a molecular mass of between 15,000 and 600,000 g/mol, contains at least 70% of monomer units derived from monomers for which the homopolymers are hydrophobic and have a glass transition temperature of greater than 40° C., also contains at least one “monomer unit” derived from an at least partially neutralized ionic hydrophilic monomer, and has an overall glass transition temperature of greater than or equal to 45° C., and being in the form of a water-in-oil emulsion or a multiple emulsion.