Graft polymers whose grafting base is selected from the group consisting of polymers having vinylamine units, polyamines, polyamidoamines and polymers of ethylenically unsaturated acids and which comprise exclusively oligoalkylenimine side chains as side chains, process for the preparation of graft polymers having oligoalkylenimine side chains, at least one oligoalkylenimine which comprises a terminal aziridine group being grafted onto one of said grafting bases, and the use of the graft polymers thus obtainable as process chemicals in the production of paper, as antimicrobial coating materials, as builders in detergents and for the treatment of metal surfaces.