The paper presents a numerical study of natural convection in the liquid-phase epitaxy (LPE) of ternary compounds. 2D computer simulation of LPE techniques that make use of dissolution of the substrate prior to growth is carried out. The computed data allow to specify the region of experimental conditions, such as melt thickness, cooling rate, initial superheating, etc., that are favorable for obtaining epitaxial hetero structures with a uniform thickness and a homogeneous composition distribution across the substrate area. (C) 2004 Elsevier B.V. All rights reserved.