Epitaxial AlN films have been grown on SiC substrate by molecular beam epitaxy (MBE) and migration-enhanced epitaxy (MEE) using radio frequency (RF) plasma-excited nitrogen. In the RF-MBE growth, the growth rates have been found to be almost constant and the crystal quality improved with increasing the substrate temperature up to 850 degreesC. Further increases of substrate temperature decreased the growth rate and degraded the crystal quality. Using the optimum substrate temperature of 850 degreesC and optimizing the shutter open time, smooth AIN films with atomic force microscope roughness as low as 0.2 nm have been grown by RF-MEE growth.