A process for the hydrolysis of polymers comprising vinylcarboxamide units by heating polymers comprising vinylcarboxamide units in an aqueous medium in the presence of acids or bases, wherein an aqueous solution or dispersion of a polymer comprising vinylcarboxamide units and an aqueous solution or a base or acid are fed continuously to a tubular reactor at elevated pressure, from 0.05 to less than one equivalent of a base or acid being used per vinylcarboxamide equivalent and the mixture being passed through the tubular reactor at a temperature of >100° C. to 250° C., depressurized and cooled.