Process for forming and applying a hydrophilic coating, which is highly slideable when wet, to a plastic or metal part either directly, or indirectly via plastic film, to a safety razor or razor blade unit, in which a solution containing a water-soluble polymer is applied to the plastic or metal part and is cured. The invention also relates to a razor blade unit comprising a blade platform for at least one razor blade, a surface for slidably engaging the skin of a user and a coating on the surface for increasing the slideability of the surface. The coating comprises a water-soluble polymer or copolymer of poly-N-vinylpyrrolidone, at least one radically polymerizable vinyl monomer and a photoinitiator.