The controlled growth of SiC heteropolytypic structures consisting of hexagonal (alpha-) and cubic (3C-) polytypes has been performed by solid-source molecular beam epitaxy. On on-axis substrates, 4H/3C/4H-SiC(0001) and 6H/3C/6H-SiC(0001) structures were obtained by first growing some nanometers thick 3C-SiC layer at lower temperatures (1550 K) and Si-rich conditions, and subsequent growth of alpha -SiC on top of the 3C-SiC layer at higher temperatures (1600 K) under more C-rich conditions. On off-axis substrates, multi-heterostructures consisting of 4H/3C- or 6H/3C-stacking sequences were also obtained by first nucleating selectively wire-like 3C-SiC nuclei on the terraces of well-prepared off-axis alpha -SiC(0001) substrates at low T (< 1500 K). Next, SiC was grown further in a step-flow growth mode at higher T and Si-rich condition. After the growth many wire-like regions consisting of 3C-SiC were found within the hexagonal SiC layer material matrix indicating a simultaneous step-how growth of both the cubic and the hexagonal SiC material.