Substrate‐stabilized, metastable, single‐crystal Ge1−xSnxfilms can be grown by molecular‐beam epitaxy (MBE). We have grown for the first time single crystal Ge1−xSnxalloys on lattice matched GaSb (withx=0.5) and InP (withx=0.26) substrates up to a thickness of 0.3 μm. Reflection high‐energy electron diffraction (RHEED) observations and x‐ray measurements show that even at very small lattice mismatch (less than 0.05%), single crystal Ge1−xSnxfilms cannot be grown thicker than 0.3 μm. Our x‐ray results suggest that the critical thickness of α‐Sn and Ge1−xSnxsingle crystal films is mainly determined by a phase transition mechanism, and the dislocation generation equivalent critical thickness is an overestimate. Under practical MBE growth conditions, it is very difficult to grow thick films, due to the sensitivity of the critical thickness to composition fluctuations. We have shown that even under an exact lattice match between substrate and film, the critical film thickness is limited.