Heteroepitaxy of GaN on both Si(00l) and (111) substrates was investigated by atmospheric pressure organometallic vapor phase epitaxy. GaN layers on Si were deposited using an epitaxially grown intermediate layer of y-AbO3. When Si(00l) was used as the substrate, highly oriented polycrystalline GaN was obtained. On the other hand, single crystalline GaN layers could be obtained on Si (1 1 1) substrates with an epitaxial relationship of GaN(000l)I r-AlzOil l l)ISi(l 11) and GaN [2 -1- 1 0] II y -Al2O3 [1 -10] II Si [1 -10]. GaN epilayers on Si(l 11) with a y -AlzO3 intermediate layer indicated a (0002) X-ray rocking curve linewidth of 1000 arcsec and strong near band-edge photoluminescence without deep-level-related emission. The photoluminescence linewidth was comparable to that of GaN grown on sapphire substrate.