The method for growing heteroepitaxial multiconstituent material on a substrate comprises deposition of a thin disordered layer of a "template-forming" material, i.e., material containing at least one constituent of the multiconstituent material to be grown, and differing in chemical composition from at least the substrate material, on the substrate surface at a relatively low deposition temperature, raising the substrate temperature to an intermediate transformation temperature, thereby causing the template-forming material to undergo a reaction that results in formation of "template" material, typically material having substantially the same composition as the multiconstituent material to be grown. Onto the thus formed template layer is then deposited the material for the epitaxial multiconstituent layer. This general process is exemplified by the growth of NiSi.sub.2 on a Si substrate, by first depositing at room temperature about 18.ANG. of Ni (the template-forming material), onto an atomically clean and undamaged Si(111) surface, heating the substrate to about 500.degree. C. for about 4 minutes (thereby reacting the Ni with Si from the substrate to form template material), followed by deposition, onto the now template-covered substrate, of about 250.ANG. of Ni at a rate of about 2.ANG./sec, with the (template-covered) substrate maintained at about 775.degree. C. The inventive method has wide applicability, and permits, inter alia, growth of essentially perfect epitaxial CoSi.sub.2 or NiSi.sub.2 on Si(100). Material grown by the method can be in form of an essentially continuous layer or a patterned layer, and can serve as the substrate for the growth thereon of further epitaxial material of different chemical composition.