Copolymers which contain a) from 2 to 50 mol % of vinyl alkyl ethers having 3 to 30 carbon atoms in the molecule, b) from 10 to 88 mol % of monoethylenically unsaturated dicarboxylic anhydrides and c) from 10 to 88 mol % of dialkyl esters of monoethylenically unsaturated dicarboxylic acids as typical monomer units in polymerized form are prepared by copolymerizing the monomers a), b) and c) at from 40.degree. to 180.degree. C. in the presence of free radical initiators and are used as film-forming resins in hair sprays and, in the form of the alkali metal, ammonium or alkaline earth metal salts, as thickeners for aqueous systems, such as cosmetic and pharmaceutical formulations, textile print pastes, liquid detergents and cleaning agents.