The molecular beam epitaxial growth of Si on SiC(0 0 0 1), exhibiting the Stranski-Krastanov mode, was investigated by reflection high-energy electron diffraction (RHEED). In the initial stage some irregular RHEED oscillations were observed corresponding to both the occurrence of surface superstructures and monolayer coverages. After exceeding a critical coverage, Si island Formation sets in. Two different kinds of islands m ere found with (1 1 1)/(0 0 0 1) and (1 1 0)/(0 0 0 1) epitaxial relationship. Under near equilibrium conditions, the critical coverage was found to be 1.4 monolayers and corresponds to the occurrence of a 3 x 3 superstructure remaining also as wetting layer after the island formation suggesting that the basic units (tetramers) Forming the 3 x 3 superstructures act already as nucleation sites for the islands. Island formation at high deposition rates (R) and low temperatures (T) was found to be kinetically delayed, which can be described as a function of X and the diffusivity D by the relationship t(c) proportional to rootR/D. Si islands relatively uniform in size of some nanometers and a density of 10(11)/cm(2) were obtained under these conditions. Al lon er X the critical thickness is only a function of T, indicating that the incorporation time of adatoms is the relevant time scale for surface diffusion. Ordered arrays of small dots were grown by decorating the steps on vicinal surfaces with Si islands.