The growth and structure of Si- and Ge-nanocrystals was investigated using high resolution X-ray diffraction (HRXRD) and atomic force microscopy (AFM). AFRI-images were used to determine the lateral and vertical dimensions of the nanocrystal. HRXRD measurements show clearly that Si- and Ge-nanocrystals grow on 6H-SiC(0001) preferentially in two different orientations - [111] and [110] - with respect to the surface normal. The growth of Ge-nanocrystals on Si-rich 6H-SiC(0001) surfaces leads to the formation of Si/Ge-alloy nanocrystals. Both types of nanocrystals grow coherently with respect to the substrate. Hence, due to the respective lattice mismatch, the degree of coherence was found to be much better for Si-nanocrystals.