This invention relates to a cleaning composition comprising at least one surfacatant or at least one cosmetic vehicle and a water-soluble or water-dispersible copolymer comprising, in the form of polymerized units: (a) at least one monomer compound of general formula I: (b) at least one hydrophilic monomer carrying a functional group with an acidic nature which is copolymerizable with (a) and which is capable of being ionized in the application medium; (c) optionally at least one hydrophilic monomer compound with ethylenic unsaturation with a neutral charge, carrying one or more hydrophilic groups, which is copolymerizable with (a) and (b).