Submicrosized alloy cables of ZnO/w-ZnS1-xSex (0 < x < 1) and ZnO/s-ZnSe1-xTex (0.8 <= x < 1) have been prepared. The lattice parameters of the sheath show linear compositional dependence following Vegard's law. The composition-band gap dependence follows the trend of E-g(ZnO/w-ZnS1-xSex)(X) = 3.60 - 1.77x + 0.87x(2) (0.22 <= x <= 1), E-g(ZnO/w-ZnS1-xSex) = .3.25 eV (0 <= x <= 0.22), and E-g(ZnO/s-ZnSe1-xTex)(X) = 2.65 - 1.82x + 1.41x(2) (0 <= x <= 1), respectively. The continuous band-gap modulations on ZnO-based heterostructures are associated with the core/sheath morphology and the nature of the sheath alloys.