Silicon carbide is a promising semiconductor for high temperature and power electronics. Its growth process has been refined continuously in the last years but there is still little knowledge on the surface processes taking place during growth. This thesis is dealing with these processes by analysing the initial growth of on-axis crystals. The growth rate limiting step of the physical vapour transport technique is determined. The study of nuclei occasionally observed gives insight on the present Ehrlich-Schwoebel barriers and allows furthermore to estimate the order of magnitude of the surface diffusion length. For the first time the growth laws of spirals on both Si- and C- face SiC surfaces are systematically analysed. Simulations are performed in order to check the influence of a limited domain size and overlapping diffusion fields on the spiral shapes and growth laws. A novel spiral step structure is observed on C-face spirals. The top bilayer dissociates under certain and reproducible conditions. The experimental parameters are reported and further analysis of this new step structure is performed.