Abstract: A process for the production of paper, board and cardboard by draining a paper stock containing interfering substances in the presence of polymers which contain vinylamine units and which have an average molar mass Mw of at least 1 million, a high-consistency stock first being prepared, at least one polymer containing vinylamine units and having an average molar mass Mw of at least 1 million and a degree of hydrolysis of from 1 to 20 mol % being metered into the high-consistency stock, the high-consistency stock being diluted to a low-consistency stock by adding water, and the low-consistency stock being drained, the polymers being hydrolyzed homo- or copolymers of N-vinylcarboxamides additives for reducing deposits in the wire part, press section and drying section of paper machines.