The nucleation and growth process of GaAs on Si has been studied by auger electron spectroscopy and transmission electron microscopy. At growth temperatures above 120 degree C, epitaxial growth begins with island formation, the size of which depends on the growth temperature. At low growth temperature (approximately 120 degree C) the epitaxial islands grow preferentially on Si surface terraces rather than on steps, and misfit dislocations are introduced at steps where the leading edges of growing islands come into contact with each other.