The invention relates to cationic block copolymers of formula A(--X--B).sub.n or C(--Y--D).sub.m, wherein A represents a hydrophilic polymer, B represents polyethyleneimine (PEI), X represents a bridge, n represents 1-200, C represents PEI, D represents the residue of a polyethylene glycol, Y represents a bridge and m represents 1-200. The invention also relates to methods for producing the inventive cationic block polymers and to their use e.g. as a tenside and for complexing nucleic acids.