The electronic structure of the (Zn, T)O (T = V, Fe, Co) diluted magnetic semiconductors is investigated theoretically from first principles, using the fully relativistic Dirac linear muffin-tin orbital band structure method. The X-ray absorption spectra, X-ray magnetic circular dichroism spectra at the Co, Fe and VL_2,3 edges are investigated theoretically. The origin of the dichroism spectra in such compounds is examined. Using the magnetic force theorem, as it is implemented within the multiple scattering theory, the exchagne interaction parameters for the transition metal atoms are calculated.