The invention relates to the following: a method for step-by-step alkylation of primary polymeric amines by step-by-step deprotonation with a metallo-organic base and a subsequent reaction with an alkyl halide; a method for modifying tertiary polymeric amines with other functional groups; polymers with secondary/tertiary amino groups and with quaternary ammonium groups; polymers with secondary/tertiary amino groups and other functional groups, especially cation exchanger groupings; membranes consisting of the above polymers, either non-crosslinked or ionically or covalently cross-linked; acid-base-blends/membranes, and a method for producing same, consisting of basic polymers with polymers containing sulphonic acid, phosphonic acid or carboxyl groups; the use of ion exchanger polymers as membranes in membrane processes, e.g., polymer electrolyte membrane fuel cells, direct methanol fuel cells, redox batteries, or electrodialysis; the use of the inventive hydrophilic polymers as membranes in dialysis and reverse osmosis, nanofiltration, diffusion dialysis, gas permeation, pervaporation and perstraction.