The invention relates to bodies coated with a hard material, comprising a multi-layer coating system containing at least one Ti1-xAlxN hard material coating and to a multi-stage CVD method for producing the bodies. The aim of the invention is to achieve excellent adhesion of the Ti1-xAlxN hard material coating in bodies coated with a hard material comprising a multi-layer coating system containing at least one Ti1-xAlxN hard material coating and a high degree of wear resistance. According to the invention, the bodies coated with a hard material comprising a multi-layer coating system containing at least one Ti1-xAlxN hard material coating are characterized by the following features: the coating system consists of a) a bonding coating applied to the body, consisting of TiN, Ti(C,N) or TiC; b) a phase gradient coating that is applied to the bonding coating; and c) the single or multi-phase Ti1-xAlxN hard material coating or coatings applied to the phase gradient coating. The phase gradient coating consists of a TiN/h-AlN phase mixture on the side facing the bonding coating and has an increasing phase fraction of fcc-TiAIN with an increasing coating thickness, (the fraction being >50%), towards the Ti1-xAlxN hard material coating(s) and a corresponding simultaneous decrease in the phase fractions of TiN and h-AlN. The coating according to the invention can be used in particular for tools and components consisting of steel, hard metals, cermets and ceramics, such as for example drills, milling cutters and indexable cutting inserts.