Very thin Au layers were deposited on SiC hexagonal and SiO2 substrates by sputtering. The Au surface diffusion, clustering, and self-organization of Au nanoclusters on these substrates, induced by thermal processes, were investigated by Rutherford backscattering spectrometry, atomic force microscopy, scanning electron microscopy, and transmission electron microscopy. On both types of substrates, clustering is shown to be a ripening process of three-dimensional structures controlled by surface diffusion and the application of the ripening theory allowed us to derive the surface diffusion coefficient and all other parameters necessary to describe the entire process. The system Au nanoclusters/SiC and Au nanoclusters/SiO2 are proposed as nanostructured materials for nanoelectronic and nanotechnology applications.