Axial nanowire heterostructures composed of cadmium sulfide (CdS)/copper indium diselenide (CuInSe2) and copper indium telluride (CuInTe2)/copper indium diselenide (CuInSe2) were synthesized by a solution-liquid-solid (SLS) method with the catalyzer of bismuth nanocrystals. Electron microscopy and diffraction studies show CuInTe2 and CuInSe2 segments growing along the [112] direction with a clear epitaxial interface between them. In CdS/CuInSe2 nanorod heterostructures, CuInSe2 and CdS segments grow along the [112] and [111] direction, respectively, with an obvious epitaxial interface between them. Energy-dispersive X-ray spectrometry demonstrates the alloy-free composition modulation in two nanorod heterostructures. In CuInTe2/CuInSe2 nanorod heterostructures, Te and Se are localized in CuInTe2 and CuInSe2 segments, respectively. Cu/In/Se and Cd/S are localized in the CuInSe2 and CdS sections of the CdS/CuInSe2 nanorod heterostructures. This research confirms that the SLS mechanism provides a general alternate technique to prepare multicomponent axial 1D heterostructures that have been difficult to generate by using either catalyst-free solution-phase synthesis or vapor-liquid-solid growth.