We have investigated the stabilization of GexSn1-x on (001) InSb substrates, as well as InSb coated GaAs substrates. We find that alloys up to ≈1500Å can be stabilized when 0 <x < 0.13. Single crystal, twinned material has been grown forx = 0.16, but only for thicknesses up to 500Å. Forx < 0.13, reflection high energy electron diffraction (RHEED) patterns reveal four stages of growth: quasi-two-dimensional growth, threedimensional growth, twinned growth, and finally phase separated growth. Ion channeling (001) results support the RHEED data, showing that film quality degrades with increasing thickness. Double and triple crystal x-ray diffraction results indicate that 1200Å-thick GexSn1-x films have excellent crystallinity forx < 0.10. Forx > 0.10, we observe partial phase separation into coherent α-Sn and α-GeSn. The films are stable in the temperature range of 125-130° C, depending on Ge concentration. We present a thermodynamic model which exhibits the trends observed in the growth and stability of epitaxially stabilized GexSn1-x alloys. Electrical and optical measurements show consistently high carrier concentrations (1021 cm-3) and low carrier mobility (<1000 cm2/ Vsec) for the alloys.