AlxGa1-xN films were grown by plasma-assisted molecular-beam epitaxy on (0001) sapphire substrates under Ga-rich conditions. To control the AlxGa1-xN composition over the entire range, the Al and Ga arrival rates were fixed while the nitrogen arrival rate was varied. We have found that the Al fraction increased with decreasing N flow due to preferentially favorable bonding of Al and N over Ga and N. Consequently, the growth rate decreased as the Al mole fraction increased. A photoluminescence quantum efficiency at 15 K was markedly higher for the AlxGa1-xN layers grown under Ga-rich conditions (3%–48%) compared to the layers grown under N-rich conditions (1%–10%), indicating much reduced nonradiative recombination in samples grown under Ga-rich conditions. © 2002 American Institute of Physics.