We have formulated a CEF (compound energy formalism) model with four sublattices to describe the Ti – TiC – TiN – TiO system. The enthalpies of all the end members have been calculated with accurate first principles methods and the site occupancies can then be obtained within the CEF model. This enables us to analyse for example how O dissolves into TiC or how C and N mix in the carbonitride. The next step is to try to refine the ab initio based CEF model by assessing experimental results and comparing with existing descriptions.