We have succeeded in growing compositionally homogeneous In0.3Ga0.7As single crystals by a newly developed growth method, the traveling liquidus-zone method. In this method, a narrow liquidus-zone saturated by a solute is formed under a relatively low temperature gradient. Since the solubility depends on temperature, solute concentration gradient at the freezing interface is established. The concentration gradient causes diffusion of the solute towards a low concentration side. At the freezing interface, crystal growth proceeds due to the decrease of solute, while solute concentration increases at the opposite side of the zone and part of the remaining feed is dissolved. Thus, the zone travels under the temperature gradient spontaneously. When we translate the sample in accordance with this spontaneous zone traveling rate, solute concentration and temperature at the freezing interface art: kept constant and long homogeneous mixed crystals can be grown. The experimentally determined appropriate sample translation rate was about 0.25 mm/h at a temperature gradient of 20 degreesC/cm. Homogeneous crystals longer than 30 mm were obtained. Although 15-20 mm long single crystals were obtained for diameters ranging fi om 1.6 to 2.0 mm, polycrystallization occurred for larger diameter crystals such as d = 14.5 mm.