The electronic properties of Ge/Ge1-x-ySixSny strained-layer heterostructures are predicted theoretically. It is found that a lattice-matched system with fully strained Ge layers and relaxed Ge1-x-ySixSny alloys can have a direct fundamental bandgap with spatial localization in the Ge layers (type I). The Si and Sn concentrations for which such a direct bandgap obtains are close to those that have already been experimentally demonstrated [ M. Bauer, C. Ritter, P. A. Crozier, J. Ren, J. Menendez, G. Wolf, and J. Kouvetakis, Appl. Phys. Lett. 83, 2163 (2003) ]. The required level of tensile strain in the Ge layers is compatible with Si–Ge technology. The predicted direct bandgap values are as high as 0.6 eV.