InN films were grown directly on sapphire (0001) substrates by rf-MBE. In the direct growth of InN on sapphire substrates without nitridation process, InN films have the tendency to form a multi-domain structure due to in-plane rotation and they can have both the epitaxial relationship of [112 0] InN || [112 0] sapphire and [101 0] InN || [112 0] sapphire . The domain with [112 0] InN || [112 0] sapphire is mainly observed at relatively low growth temperatures around 520 C. The domain with [101 0] InN || [112 0] sapphire , however, becomes dominant with increasing the growth temperatures to around 540 C. The dominant factor in determining the main epitaxial relationship is found to be its growth temperature. However, this is highly sensitive to a small change in growth temperature which should be controlled within 20 C.Introduction Group-III nitride semiconductors are attractive materials for optoelectronic devices in visible and ultraviolet regions and for electronic devices that can operate at high-temperature, high-frequency and high-power conditions. In spite of these attentions, study on InN, particularly, has been far behind the other group-III nitride semiconductors such as GaN and AlN because the growth of InN is very difficult, which is attributed to its low dissociation temperature [1]. Recently, epitaxial growth of high quality InN, with good surface morphology and a high electron mobility, was reported [2, 3]. However, the growth mechanism of InN, especially the epitaxial relationship of a-axis between InN films and sapphire substrates, is not fully clarified. When InN films were grown on sapphire (0001) substrates with nitridation process, the epitaxial relationship has been found as [101 0] InN || [101 0] AlN || [112 0] sapphire [4]. On the other hand, when InN films were grown directly on sapphire (0001) substrates, some different results have been obtained. Yamaguchi et al. [5] reported that InN films with the epitaxial relationship of [101 0] InN || [112 0] sapphire were obtained when they were grown at 450 C by metalorganic vapor phase epitaxy (MOVPE). On the other hand, Guo et al. [6] reported that InN films, which were grown at 500 C by microwave-excited metalorganic vapor phase epitaxy (ME-MOVPE), were with [112 0] InN || [112 0] sapphire . In addition, Wakahara et al. [7] reported that InN films grown by ME-MOVPE were with two epitaxial relationships of [101 0] InN || [112 0] sapphire and [112 0] InN || [112 0] sapphire . It has not been clear yet what has led to these different results on the epitaxial relationship.Various parameters, such as growth method, growth process, substrate temperature and V/III ratio should be considered.