The invention relates to powder-coated substrates bearing on a powder-coated surface a scratch-resistant and abrasion-resistant topcoat of a coating material which comprises: a) condensates based on hydrolyzable silanes containing at least one non-hydrolyzable substituent, the hydrolyzable silanes having an epoxide group on at least one non-hydrolyzable substituent; b) a curing catalyst selected from Lewis bases and alkoxides of titanium, zirconium or aluminium; c) nanoscale particulate inorganic solids having a particle size in the range from 1 to 100 nm; and d) at least one organic monomer, oligomer or polymer containing at least one epoxide group.