Hardness, oxidation resistance and adhesion have traditionally been the most important parameters for material selection and optimization of hard, wear resistant coatings. More recently, thermal conductivity has become a focus of research, as it has the potential to have a significant effect on coating performance. Even though new experimental methods have become available to characterize thermal conductivity, recent studies focused on existing material systems, and there have been few attempts to design coating thermal conductivity for specific applications. We study thermal conductivity of arc evaporation oxynitride coatings with the composition CrN1 - xOx and TiN1 - xOx (x = 0 ... 0.4). With increasing substitution of nitrogen by oxygen, thermal conductivity could gradually be reduced from 9W m(-1) K-1 to 2.5W m(-1) K-1 in CrN1 - xOx and from 35 to 5W m(-1) K-1 in TiN1 - xOx. A model that assumes a constant phonon scattering cross-section of the oxygen concentration can explain the observed functional relationship. Other properties such as thermal stability, oxidation resistance and hardness of these oxynitrides show little variation with oxygen concentration, clearing the way to design functional coatings with specific thermal properties. (C) 2013 Elsevier B.V. All rights reserved.