The self-consistent band structure, total and partial density of states for the stable compounds hcp-WC and MoC are calculated by the LMTO-ASA method based on Kohn-Sham's LDF theory. On the basis of theoretical parameters obtained from our ab initio calculations, the total and partial electronic pressure, the electron-ion interaction constant η, electron- ph-onon coupling constant λ and superconducting transion temperature Tc are studied. The theoretical results have been verified by both the experimental photoemission spectra and ground-state properties, as well as the superconductivity data.