We report the synthesis and characterization of radial heterostructures composed of an antimony telluride (Sb2Te3) core and a germanium telluride (GeTe) shell, as well as an improved synthesis of Sb2Te3 nanowires. The synthesis of the heterostructures employs Au-catalyst-assisted vapor-liquid-solid (VLS) and vapor-solid (VS) mechanisms. Energy-dispersive X-ray spectrometry indicates that Sb and Ge are localized in the Sb2Te3 and GeTe portions, respectively, confirming the alloy-free composition in the core/shell heterostructures. Transmission electron microscopy and diffraction studies show that Sb2Te3 and GeTe regions exhibit rhombohedral crystal structure. Both Sb2Te3 and GeTe grow along the [110] direction with an epitaxial interface between them. Electrical characterization of individual nanowires and nanowire heterostructures demonstrates that these nanostructures exhibit memory-switching behavior.