We summarize our results on plasma-assisted molecular beam epitaxy of cubic GaN on GaAs(001) and on Si(001) and of hexagonal GaN on 6H-SiC(0001) with emphasis on the nucleation process. A two-step growth sequence must be used to optimize and Control the nucleation and the subsequent growth independently. While a perfect epitaxial orientation exists for GaN-on-GaAs due to the coincidence lattice relationship of the two constituents. The same effect is impeded for GaN-on-Si by the growth of SixNy inclusions at the interface which act as nucleation cores for the formation of the hexagonal GaN phase. A suitable template, such as a thin GaAs or SiC insertion layer, avoids formation of the SixNy inclusions. Finally, growth of hexagonal GaN-on-6H-SiC without any buffer layer requires very careful adjustment of the N-to-Ga flux ratio and the substrate temperature, independently for the nucleation stage and for the subsequent layer-by-layer growth. The structural perfection and the optical properties of the resulting 1 mu m thick GaN films then reach state-of-the-art quality even without a buffer template.