The structural, electronic and elastic properties of TiC x N 1− x , TiC x O 1− x and TiO x N 1− x alloys have been investigated by using the plane-wave pseudopotential method within the density function theory. The present lattice parameters and bulk modulus of TiC x N 1− x alloys generally follow the Vegard’s law. The elastic properties of TiC x N 1− x alloys presented as a function of concentration reveal the anisotropy and ductility. The prediction of elastic properties for TiO x N 1− x alloys has been presented due to the consistency between the calculated results and the experimental results for TiC x N 1− x and TiC x O 1− x alloys. The partial density of states (PDOS) and total density of states (DOS) for the binary and ternary compounds have been obtained, and the metallic behavior of these alloys has been confirmed by the analysis of DOS.