The ab initio pseudopotential method within the local density functional theory and virtualcrystal approximation is used to study the band gap of the Si1−x−yGexCy (y 0.09) alloys on a Ge (001) substrate. The heterojunction discontinuities are also investigated in the framework of the average bond energy theory in conjunction with the deformation potential method. The calculated results show that the energy gap still remains indirect and only a small amount of C could cause the energy gap to be shrunk signi cantly. The top of the valence bands of the strained Si1−x−yGexCy alloys on Ge (001) is signi cantly lifted and even could be greatly higher than that of Ge by the addition of small amounts of carbon. The trends of our results are consistent with other theoretical data.