A process for producing an isobutene copolymer derivative by: (I) free-radically copolymerizing (a) 10-90 mol % of a monoethylenically unsaturated C4- to C12-dicarboxylic acid, anhydride, or ester, (b) 10-90 mol % of a high-reactivity isobutene polymer having Mn=110-250000 and obtained by polymerizing isobutene in the presence of an iron-halide-, aluminum trihalide-, or alkylaluminum halide-donor complex, each donor being an ether or carboxylic ester function, or in the presence of a Lewis acid complex containing an organic sulfonic acid, and (c) 0-50 mol % of a monoethylenically unsaturated compound copolymerizable with (a) and (b), to obtain an intermediate isobutene copolymer; and (II) reacting the carboxylic acid functions in the intermediate with at least one of ammonia, an amine, and an alcohol, to form a moiety containing at least one of a hydroxyl, carboxylic ester, amino, quaternized amino, amido, and imido group.