In this paper we present the detailed thermodynamic analysis and experimental study on the MBE growth process of heteroepitaxial InSb layers on strongly lattice-mismatched GaAs(100) and Si(100) substrates. A good qualitative agreement between theoretical and experimental results has been obtained. The influence of growth parameters (T s u b , Sb 4 /In flow ratio) on the structural, electrical, and luminescence characteristics of the layers has been also investigated. The increase of T s u b from 350 to 420°C together with the Sb 4 /In flow ratio reduction result in a mirror-like surface morphology, decrease in X-ray rocking curve FWHM values and dislocation density down to 210 arcsec and 1 10 8 cm - 2 , respectively, and the disappearance of stacking faults. It also provides a lower unintentional doping level (n∼2.8 10 1 6 cm - 3 ) in undoped layers and a higher electron mobility (51000 cm 2 /V s at 300 K and 36000 cm 2 /V s at 77 K). Using Be as a p-type dopant has been shown to enable to reach readily the Be doping level of InSb/GaAs and InSb/Si as high as 2 10 1 9 cm - 3 .