The invention relates to a process for producing water-soluble or water-swellable polymer products from acrylic acid and/or acrylic acid derivatives partially or completely neutralized with nitrogen compounds and with exceedingly low levels of residual monomers, which process is characterized by subsequent heating of the polymer product at temperatures of from 120 to 240 C. The polymers produced accordingly are suitable for use as flocculants, dispersants and absorbers.