A polymeric material, in particular a polymeric material manufactured by polymerisation or polyaddition, for example polyolefins or polyurethanes, in particular polyethylene, with an antimicrobial surface.The polymeric material contains a maximum of 0.1% by weight of fatty acid ester, a maximum of 0.1% by weight of superacid counter-ions and between 2.5% by weight and a maximum of 10% by weight, preferably a maximum of 5% by weight, of at least one compound (1) which brings about the antimicrobial action.This compound (1) consists of at least one antimicrobially effective hydrophilic molecular group (2) and at least one molecular group (4) which causes physical anchoring of the compound (1) in the polymeric material (3).