The growth of certain SiC polytypes in the solid-source molecular beam epitaxial growth (MBE) process has been analysed within the framework of classical thermodynamic nucleation theory. It has been demonstrated that the formation of certain polytypes in the nucleation stage is due to a complex interplay between their differences in the surface and formation energy as well as the growth conditions. Based on these considerations, the growth conditions have been estimated quantitatively which show a preference for certain polytype on the SIC(0 0 0 1) Si-face. The estimations clearly indicate that the formation of a polytype in the nucleation stage is determined by a set of growth parameters: substrate temperature, Si/C-ratio and C-flux. The nucleation of the cubic 3C-SiC polytype was found to be preferred generally under conditions of high supersaturation or large Si/C-ratio, while the formation of 4H-SiC is more favoured at low supersaturations and more C-rich conditions. 6H-SiC or 15 R-SiC should occur under conditions in between them. Considering a stronger relaxation of the C-face in comparison to the Si-face, the formation of 4H-SiC is clearly preferred on the (0 0 0 1) C-face in a wider range of growth conditions, while the probability of 3C-SiC nucleation is much lower than on the Si-face. Moreover, an increase in temperature also increases the nucleation probability of the hexagonal polytypes. The obtained results agree very well with experimental findings based on SiC-bulk sublimation growth experiments as well as with results recently obtained by MBE.