The present invention relates to a process for coating substrates, which comprises the steps: a) provision of a substrate, b) application of a composition to at least one surface of the substrate, the composition comprising a silane of the general formula (Z1)Si(OR3), where Z1 is OR or Gly (Gly=3-glycidyloxypropyl) and R is an alkyl radical having from 1 to 6 carbon atoms and all radicals R can be identical or different, an inert solvent and an initiator and the inert solvent having a boiling point under the drying conditions of step c) which is in a range from 50° C. above to 50° C. below the drying temperature of step c) and the boiling point of the inert solvent under the drying conditions of step c) being at least 80° C., and c) drying of the composition applied in step b) at a drying temperature of from 100° C. to 250° C., and also to a coated substrate obtainable by means of the abovementioned process.