Substrate comprising an abrasion-resistant diffusion barrier layer system

The invention relates to a substrate, comprising an abrasion-resistant diffusion barrier layer system. Said system consists of a hard base layer which contains a coating composition based on compounds that can be thermally or photochemically cured to a polymer or compounds that can be polymerized and a nanostructured cover layer which can be obtained by the application of a nanoscalar mass containing sol and/or solid particles to the base layer that still has reactive surface groups and by subsequent thermal treatment or curing. The coating system is characterised by a high resistance to abrasion and a diffusion barrier action and is particularly suitable for use as a protective layer for synthetic substrates.