The invention relates to coated bodies made of metal, hard metal, cermet or ceramic material, coated with a single- or multi-layer coating system containing at least one hard material composite coating, and to a method for coating such bodies. The aim of the invention is to develop a coating system for such bodies, which is single- or multi-layered and comprises at least one hard material composite coating, which contains cubic TiAlCN and hexagonal AlN as the main phases and is characterized by a composite structure having a smooth, homogeneous surface, high oxidation resistance and high hardness. The aim includes the development of a method for cost-effectively producing such coatings. The hard material composite coating according to the invention contains cubic TiAlCN and hexagonal AlN as main phases, wherein the cubic TiAlCN is microcrystalline fcc-Ti1-xAlxCyNz where x>0.75, y=0 to 0.25 and z=0.75 to 1 having a crystallite size of ≧=0.1 μm, and wherein the composite coating in the grain boundary region additionally contains amorphous carbon having a percent by weight of 0.01% to 20%. The coating is carried out according to the invention in a LPCVD process at temperatures between 700° C. and 900° C. and at pressures between 102 Pa and 105 Pa without additional plasma excitation. The hard material composite coating according to the invention is characterized by a composite structure having a smooth, homogeneous surface, high oxidation resistance and high hardness and can be used in particular as a wear protection coating on Si3N4 and WC/Co indexable inserts and steel components.