In a process for preparing cationic or amphoteric (co)polymers derived from acrylamide by a Hofmann degradation reaction in aqueous solution in the presence of an alkali and/or alkaline-earth metal hydroxide and an alkali metal hypohalide on a base copolymer, a solution of base copolymer on which the reaction is performed contains a polyvalent cationic salt representing at least 0.5% by weight, preferably from 2 to 10% by weight of the base copolymer.