Polycondensate, composition containing it, especially a nail varnish composition, and process for preparation. The polycondensate may be obtained by reacting: a polyol comprising 3 to 6 hydroxyl groups; a saturated or unsaturated non-aromatic monocarboxylic acid; an aromatic monocarboxylic acid containing 7 to 11 carbon atoms; and a saturated or unsaturated, or even aromatic, linear, branched and/or cyclic polycarboxylic acid, comprising at least two carboxylic groups COOH; and/or a cyclic anhydride of such a polycarboxylic acid.