Polytypism in semiconductors including SiC and ZnS is systematically investigated using ab initio pseudopotential approach for the total energy calculations with/without vacancy in 3C (zinc blende), 6H, 4H, and 2H (wurtzite) structures. The calculated total energy E among 3C, 6H, 4H, and 2H implies that 3C and 4H are the most favorable for SiC, while ZnS prefers 3C. Furthermore, it should be noted that the energy differences Delta E among these four structures are very small without the explicit dependence on the hexagonality, whereas the Delta E strongly depends on the hexagonality for AlN and Si without polytypes. The Delta E for SiC with vacancy explicitly reveals the most stable structures, such as 6H with Si-vacancy and 4H with C-vacancy. On the other hand, ZnS with vacancy prefers 2H with S-vacancy. These results qualitatively agree well with the experimental findings, where 3C appears at low temperatures, while 6H and 4H for SiC and 2H for ZnS are favored at high temperatures enhancing vacancy formation. In particular, the calculated vacancy formation energies suggest that C- and Si-rich conditions, respectively, prefer 6H-SiC and 4H-SiC, while 2H-ZnS appears independent of conditions. Consequently, these results suggest that the vacancy formation plays an important role in the polytypism in semiconductors. (C) 2010 Elsevier B.V. All rights reserved.