The invention relates to a method for hydrophilizing surfaces of polymer workpieces. The method has a step (a) of pretreating the workpiece surfaces in a high-frequency gas plasma which is produced on the basis of an inert gas in order to clean and activate the workpiece surfaces； a step (b) of precoating the pretreated workpiece surfaces with polyacrylic acid using a high-frequency gas plasma made of a gas mixture, said gas mixture being composed of an inert gas and a first gas made of biocompatible, polymerizable carboxy group-containing monomers； and a step (c) of subsequently coating the precoated workpiece surfaces using a second gas substantially containing acrylic acid monomers.
