A cosmetic composition for hair comprises at least one branched sulfonic polyester and at least one conditioning agent such as non-volatiles silicones, cationic or amphoteric polymers and cationic or amphiphilic surfactants, in a cosmetic medium. An Independent claim is also included for an aerosol apparatus consisted of a container comprising an aerosol composition (a liquid phase, a solvent and a propeller) and a distribution system.