The invention relates to a process for the production of water-soluble or water-swellable polymers having a low content of residual monomers, particularly on the basis of acrylic acid and/or acrylamide and at least one additional water-soluble comonomer, in which process a monomer solution in a polymerizing state is treated with electromagnetic radiation at the earliest after reaching the maximum temperature of polymerization, and the gel obtained is subsequently crushed and dried, and it also relates to the water-soluble or water-swellable polymers as such, which can be obtained according to said process, to their use in the hygiene industry, packaging industry, in the agrarian technology or in agriculture and horticulture, in the cable industry and information technology, in the food industry, papermaking industry, and to their use as flocculation aids and as drilling fluid in petroleum production.