Hydrophobically modified polymers containing vinylamine or ethylenimine units and obtainable by reacting (a) polymers containing vinylamine or ethylenimine units with (b) compounds of the formula R-A-(EO, PO, BuO).sub.n--X (I), where R is C.sub.4- to C.sub.26-alkyl or C.sub.4- to C.sub.26-alkenyl, A is O, NH or COO, EO is an ethylene oxide unit, PO is a propylene oxide unit, BuO is a butylene oxide unit, n is from 1 to 250 and X is a functional group which can be covalently bonded to an OH group, process for the preparation of hydrophobically modified polymers containing vinylamine or ethylenimine units by reacting polymers containing vinylamine or ethylenimine units with a water repellent of the formula I and use of the polymers thus obtainable as an additive to paperstock in papermaking.