A cosmetic or dermatological composition comprising at least one aqueous phase, of a branched or crosslinked polymer is obtained by polymerization of an aqueous solution of one or more monomers in water-in-oil inverse emulsion, at least one of the monomers used being an acrylic monomer and one or more of the monomers used being a monomer bearing at least one weak acid function, the molar percentage of monomers bearing at least one weak acid function relative to all of the monomers used being at least 30 mol %. The polymerization is carried out with a concentration of all the monomers in aqueous solution lying in the range 1.3 mmol to 3.6 mmol per gram of aqueous solution. During the polymerization, at most 20% of the acid functions present on the monomers having at least one acid function are in neutralized form. The compositions are intended for treatment of keratinous materials.