A hard material layer system with a multilayer structure, comprising alternating layers A and B, with A layers having the composition MeApAOnANmA in atomic percent and B layers having the composition MeBpBOnBNmB in atomic percent, where the thermal conductivity of the A layers is greater than the thermal conductivity of the B layers. MeA and MeB each comprise at least one metal of the group Ti, Zr, Hf, V, Nb, Ta, Cr, Mo, W, and Al, pA indicates the atomic percentage of MeA and pB indicates the atomic percentage of MeB and the following is true: PA=PB, nA indicates the oxygen concentration in the A layers in atomic percent and nB indicates the oxygen concentration in the B layers in atomic percent and the following is true: nA