The invention relates to a process for preparing a cationically modified (meth)acrylamide polymer by the Mannich reaction. There is prepared in advance a stable aldehyde-secondary amine adduct, which is obtained as a reaction product of an aqueous solution of the secondary amine and an aqueous solution of the aldehyde, and which, after the formation of the adduct, is stabilized to endure storage, by lowering the pH of the mixture of 7 or below and/or by adding methanol, and the adduct thus prepared is added to an aqueous solution of the (meth)acrylamide polymer and the pH is adjusted to an alkaline level, whereupon modification occurs. The invention also relates to the use of the modified (meth)acrylamide polymer as a flocculation, retention or dewatering agent.