Cosmetic composition for topical or hair application. This composition contains, in a suitable cosmetic vehicle, a pseudo-latex consisting of particles of a film-forming radical polymer containing carboxylic acid functions, neutralized to a degree of neutralization between 10 and 80% using a polyfunctional neutralizing agent consisting either of a diamine or of the combination of a polyvalent metal salt and an inorganic or organic base, the average diameter of the said particles being between 10 and 450 nm. The composition preferably takes the form of a shampoo, a conditioner, a styling or treating lotion or gel or a hair shaping product, or the form of a make-up product such as a mascara or a nail varnish.