A process for producing a crystalline substrate with an optical multi-layer system thereon and the crystalline substrate obtainable thereby. The process comprises the successive application of at least two free-flowing compositions which comprise nanoscale inorganic solid particles comprising at least one of a polymerizable and a polycondensable organic group to a surface of the crystalline substrate and the polymerization and/or polycondensation of the organic groups of the solid particles to form organically crosslinked layers on the substrate and a single-stage thermal consolidation of these layers with a burnout of organic constituents thereof. The at least two compositions give rise to layers with different refractive indices.