An ab initio MO-LCAO investigation was undertaken concerning the structure and reactivity towards alkenes of model tungsten(VI) peroxo complexes derived from the tetrakis (oxodiperoxotungsto) phosphate(3-) complex, {PO4[W(O)(O-2)(2)](4)}(3-), an efficient reagent (as "onium" salt) for olefin epoxidation in nonprotic solvents, as well as a highly effective catalyst for the same reaction when used in combination with hydrogen peroxide in a two-phase system. The complex of formula [H2PO4(W2O10)](-) (A), chosen as a simplified model of the (PO4[W(O)(O-2)(2)](4)}(3-) anion, and the related "partially reduced" complexes of general formula [H2PO4(W2O9)](-)(B-1,B-2) and [H2PO4(W2O8)](-) (C1-3) were considered. The best molecular geometries for all the investigated complexes were obtained at Hartree-Fock level. using a relativistic effective potential for core electrons of the W atoms. The Hartree-Fock energies corrected for electron correlation by means of Lee-Yang-Parr density functional were used to evaluate the reaction energies regarding the peroxidic oxygen transfer from complexes A and B-1,B-2 to an alkene (ethylene). The energetics of these complexes is discussed in the framework of a global process leading to the formation of epoxide and restoring the starting complexes by reaction of the resulting "reduced" species with hydrogen peroxide. All the reaction steps, identified on the basis of a purely theoretical investigation, were found to be, to a different extent, exothermic. The analysis of the net atomic charges carried by the peroxidic oxygens in complexes A and B-1,B-2 reveals that the oxygen expected to be the "most electrophilic" is the one adjacent to the triply shared oxygen. Its transfer to ethylene is associated with the highest energy gain when complex A is involved, but such a behaviour is no longer regularly observed when a complex of type B is considered,