The thin him growth of GaN, AlGaN, and AlN on GaN/SiC substrates by molecular beam epitaxy (MBE) has been studied. The GaN/SiC substrates consisted of 3-mu m-thick GaN buffer layers grown on 6H-SiC wafers by metal organic vapor phase epitaxy (MOVPE) at Cree Research, Inc. A radio frequency plasma source was employed to generate active nitrogen species for MBE growth. The high quality of the MBE grown GaN epilayers was evident from the intense room temperature photoluminescence (PL) dominated by a sharp band-edge peak at 3.409 eV having a full width at half maximum (FWHM) of 29.7 meV and the double-crystal x-ray rocking curve (0002) diffraction peak having FWHM as narrow as 156 arcsec. Vertical cross-section TEM clearly showed these MBE grown GaN epilayers to have replicated the quality of the underlying MOVPE grown GaN buffer layer on SIG. The room temperature PL spectra from Mg doped p-type films showed a dominant peak at 3.2 eV. AlxGa1-xN films were also grown on GaN/SiC substrates. Two-dimensional nucleation and growth was monitored by reflection high energy electron diffraction for GaN, AlxGa1-xN, and AlN epilayer deposition, and featured (2 x 2) surface reconstruction during the growth of GaN/AlN strained layer superlattices. Light emitting diodes (LEDs) based on vertical AlxGa1-xN/GaN double heterostructures have been demonstrated for the first time using MBE grown III-V nitrides on conducting GaN/SiC substrate materials. The typical turn-on voltage among these LEDs was 3.2 V. The forward bias voltage was 4.7 V at 20 mA. The peak wavelength of the electroluminescence (EL) spectrum was 400 nm at 77 K. These results demonstrate that MBE may be used to produce GaN, AlxGa1-xN and AlN based epitaxial structures which are comparable in crystalline quality to those grown by MOVPE.