We have measured the time-resolved, X-ray excited optical luminescence spectra from two types of MgxZn(1-x)O core-shell, heterostructured nanowires: type I, with a small x, wurtzite core, encased in a larger x, wurtzite sheath; and type II, with a wurtzite core (x approximately 0), encased in a rock-salt sheath (x>0.62). By monitoring the X-ray energy dependence of the various luminescence peaks, we have determined the local environment of the sites where these peaks originate.