Abstract: A laminated composite material, and a method of improving the surface hardness of laminated composite materials, wherein selected regions of the carrier material of the laminated composite system are treated with high-energy beams, and the temperature control is designed in such a manner that the rays penetrate into a maximum a 0.1-fold the entire thickness of the carrier material. The temperature increase in the region of the sliding material is a maximum of 80% of the melting temperature of the lowest melting constituent of said material. The laminated composite material with a rear steel substrate surface can be post-hardened. The steel substrate has at least in one part of the surface facing away from the function layer a level of hardness increased by a factor of 1.5 or more than at a depth which corresponds substantially to 0.1-fold of the thickness of the steel substrate.