The use of acrylic acid or acrylic acid anhydride for hydrophilizing surfaces of a body comprises pre-coating the surfaces using a high frequency plasma generated from a gas mixture composed of an inert gas and a first gas formed of biocompatible, polymerizable, carboxy group-containing monomers, and then follow-up coating the precoated surfaces of the body, wherein the pre-coating takes less than 10 minutes or even less than 1 minute, and the follow-up coating is made using a second gas substantially consisting of the acrylic acid or acrylic acid anhydride monomers.
