[en] The authors perform band-structure calculations using the Green's function method in the atomic spheres approximation for titanium carbide containing isolated substitutional impurities such as nitrogen and oxygen atoms. The basic equations for the calculation are given. Histograms are presented of the total and partial densities of states N(E) of ideal TiC obtained by applying the Green's function-ASA-KKR method. Results of the calculations of the local electronic states of nitrogen and oxygen impurity atoms together with the density of states of carbon in the carbide are given. The results of the calculations are compared with the available x-ray-emission spectra of titanium oxycarbides and carbonitrides