Described are a method of killing microorganisms in aqueous industrial systems or products for industrial applications based on water by adding from 0.001 to 5% by weight of a water-soluble or water-dispersible polymer containing from 30 to 100 mol % of styrenesulfonic acid, from 0 to 40 mol % of an N-vinyllactam and/or N-vinylamine, and from 0 to 30 mol % of further free-radically polymerizable monomers as biocidal additive, and a method of protecting articles by applying an antimicrobial aqueous composition comprising such an additive.