The present invention relates to a process for coating substrates, which comprises the steps: a) provision of a substrate which is not natural stone and/or natural ashlar, b) application of a composition comprising a silane of the general formula (Z1)Si(OR)3, where Z1 is R, OR or Gly (Gly=3-glycidyloxypropyl) and R is an alkyl radical having from 1 to 18 carbon atoms and all radicals R can be identical or different, oxide particles selected from among the oxides of Ti, Si, Zr, Al, Y, Sn, Zn, Ce and mixtures thereof, with bound organic radicals SiR′3 being present on the surface of the oxide particles, where R′ has the general formula CnX1+2n where n=1 to 20, X=hydrogen and/or fluorine, all radicals R′ can be identical or different and the organic radicals SiR′3 being able to be split off, and an initiator to at least one surface of the substrate and c) drying of the composition applied in step b), and a coated substrate which can be obtained by the abovementioned process.