The invention relates to a body which is coated with hard material and has a plurality of layers applied by means of CVD, wherein the outer layer comprises Ti1-xAlxN, Ti1-xAlxC and/or Ti1-xAlxCN where 0.65≦x≦0.9, preferably 0.7≦x≦0.9, and this outer layer has compressive stresses in the range from 100 to 1100 MPa, preferably from 400 to 800 MPa, and a TiCN or Al2O3 layer is arranged under this outer layer.