Composite of shaped bodies made from wooden materials with film-shaped substrates, wherein a surface of the shaped body has a first layer comprising a crosslinked radiation-curing hot-melt adhesive, said layer is covered with a second adhesive layer of a hot-melt adhesive, and said second adhesive layer is adhesively bonded to a film-shaped substrate. A method for producing composite shaped bodies of this type is provided, in which method, as one step, the surface is coated with a UV-crosslinkable hot-melt adhesive, and which method makes in-line production of the composite bodies possible.