Synthesis of ZnO/ZnS heterostructures under thermodynamic conditions generally results in the wurtzite (WZ) structure of the ZnS component because its WZ phase is thermodynamically more stable than its zinc blende (ZB) phase. In this report, we demonstrate for the first time the preparation of ZnO/ZnS coaxial nanocables composed of single crystalline ZB structured ZnS epitaxially grown on WZ ZnO via a two-step thermal evaporation method. The deposition temperature is believed to play a crucial role in determining the crystalline phase of ZnS. Through a systematic structural analysis, the ZnO core and the ZnS shell are found to have an orientation relationship of (0002)ZnOWZ//(002)ZnSZB and [01-10]ZnOWZ//[2-20]ZnSZB. Observation of the coaxial nanocables in cross-section reveals the formation of voids between the ZnO core and the ZnS shell during the coating process, which is probably associated with the nanoscale Kirkendall effect known to result in porosity. Furthermore, by immersing the ZnO/ZnS nanocable heterojunctions in an acetic acid solution to etch away the inner ZnO cores, single crystalline ZnS nanotubes orientated along the [001] direction of the ZB structure were also achieved for the first time. Finally, optical properties of the hollow ZnS tubes were investigated and discussed in detail. We believe that our study could provide some insights into the controlled fabrication of one dimensional (1D) semiconductors with desired morphology, structure and composition at the nanoscale, and the synthesized WZ ZnO/ZB ZnS nanocables as well as ZB ZnS nanotubes could be ideal candidates for the study of optoelectronics based on II-VI semiconductors.