An improved process for the production of a substantially equimolecular copolymer of maleic acid anhydride and diisobutylene in which from 10 to 100 mole % of the anhydride groups are esterified with linear or branched aliphatic monoalcohols containing from 1 to 20 carbon atoms or with cycloaliphatic monoalcohols containing from 5 to 6 carbon atoms to form the corresponding semiesters, wherein shortly before or after the end of the solution or suspension copolymerization of maleic acid anhydride and diisobutylene a monomer corresponding to the general formula ##STR1## in which R=H, CH.sub.3, C.sub.2 H.sub.5, --OR.sub.2, --O--CO--CH.sub.3, ##STR2## --CH.sub.2 OH, --CH.sub.2 O--C--CH.sub.3, R.sub.1 =H , CH.sub.3 andR.sub.2 =a linear or branched alkyl group containing from 1 to 4 carbon atoms,Or mixtures of these monomers with one another are added to the polymerization mixture in quantities of from 1 to 12 mole %, based on the maleic acid anhydride used. The aqueous or aqueous-alcoholic alkali, amine or ammonium salt solutions of the semiesters of the copolymer are highly effective as anionic sizing agents for paper.