A process for forming UV absorber layers on an inorganic or organic substrate is described. That process comprises a) allowing a low-temperature plasma, a corona discharge or high-energy radiation to act on the inorganic or organic substrate, b) applying to the treated inorganic or organic substrate at least one free-radical-forming initiator and at least one UV absorber containing at least one ethylenically unsaturated group, and, optionally in the form of melts, solutions, suspensions or emulsions, at least one synergist and/or at least one ethylenically unsaturated compound, c) heating the coated substrate and/or irradiating it with electromagnetic waves. The invention relates also to a substrate provided with a UV absorber layer in accordance with that process. That process substantially eliminates vacuum conditions and excessive thermal stress or energy stress and also destruction of the UV absorber. Clear, transparent UV absorber layers that exhibit good adhesion are formed, the properties of which, such as, for example, the optical density, are advantageously controllable.