A process for preparing isobutene homo- or copolymer derivatives by (i) polymerizing isobutene or an isobutene-comprising monomer mixture in the presence of an iron halide-donor complex, an aluminum trihalide-donor complex, or an alkylaluminum halide-donor complex, (ii) reacting a resulting high-reactivity isobutene polymer with a compound which introduces a low molecular weight polar group or a substructure thereof, and (iii) in the case of reaction with a substructure, further reacting to complete the formation of the low molecular weight polar group. The homo- or copolymer derivatives include a radical of a hydrophobic polyisobutene polymer having a number-average molecular weight of 110 to 250 000 and low molecular weight polar groups including amino functions, nitro groups, hydroxyl groups, mercaptan groups, carboxylic acid or carboxylic acid derivative functions, sulfonic acid or sulfonic acid derivative functions, aldehyde functions and/or silyl groups.