The growth of SIC layers on hexagonal (or alpha-) SiC(0001) has been performed by solid-source MBE between 1300 and 1600 K. The alpha -SiC layers have been grown homoepitaxial via step-flow on off-axis substrates, whereas pseudomorphic cubic (or 3C-) SiC layers were obtained on alpha -SiC via nucleation and subsequent step-flow. Under more equilibrium-like conditions, 3C-layers nearly free of twin-boundaries were obtained. The SIC layers were of high quality and without unintentional doping, as revealed by photoluminescence investigations The controlled growth of SiC heteropolytypic structures consisting of hexagonal and cubic polytypes, such as 4H/3C/4H-SiC(0 0 0 1) acid 6H/3C/6H-SiC(0 0 0 1), has also been demonstrated. Such structures were obtained by changing the growth conditions from lon er temperatures (1550 K) and Si-rich Si/C ratio (3C-SiC) to higher temperatures (1600 K) and more C-rich Si/C ratio. On off-axis substrates, such heterostructures were also obtained by first nucleating selectively wire-like 3C-SiC nuclei on the terraces of well-prepared alpha -SiC(0 0 0 1) substrates at low T (< 1500 K) and a subsequent step-flow of both the 3C wires and the surrounding alpha -SiC material.