We report studies of the interface formed when InSb is deposited onto a CdTe substrate in a molecular beam epitaxy chamber and elucidate conditions under which epitaxial growth is possible. We find that a necessary condition for epitaxy at a substrate temperature Ts is that the growth rate exceed a minimum value Ω min (T s ). Reflection high energy electron diffraction patterns taken in situ and transmission electron micrographs taken ex situ show that interfaces formed when Ω > Ω min have a short period roughness which is independent of the Sb/In flux ratio and which diminishes with increasing Ω. Raman spectra show no evidence of interfacial compounds. An analysis of Auger spectra of thin layers of InSb grown on CdTe indicates the existence of Te at the surface of the InSb but not in the layer itself. The Te concentration is found to decrease with InSb layer thickness. We propose a model based on a competition between the reaction of free In and Sb with the CdTe surface and the nucleation and growth of InSb. We use this model to account for the existence of Omin, interface roughness, and the presence of Te at the surface of the InSb epilayer.