We have used low pressure MOVPE to grow a series of short-period ZnSe-ZnTe strained-layer superlattices onto either ZnSe or ZnTe buffer layers. Typical superlattice periods range from 2 to 6.5 nm with constant ZnSe thickness of 2 monolayers. X-Ray diffraction analyses have shown that the superlattices are free-standing if grown on a ZnSe buffer but lattice matched to ZnTe if grown on ZnTe buffer layers. The luminescence emitted by the free standing samples has been studied using both the photoluminescence technique at low temperature and cathodoluminescence at higher temperature, for improved pumping. Our samples exhibit a complicated temperature dependence similar to the behaviour of ZnSeTe alloys where exciton self-trapping to tellurium gives strong photoluminescence bands labelled SI and S2. A high temperature, high energy feature is observed and is associated with the fundamental superlattice transition. The energy position of this structure suggest a high value of the ZnSe/ZnTe valence band offset, in the range 1200-1400 meV.