The roles of chemical composition (X, M and M(FW)) of di-transition-metal-substituted gamma-Keggin polytungstates and polymolybdates, [(X(n)(+)O(4))M(2)(OH)(2)(M(FW))(10)O(32)]((8-n)-), on the geometry, electronic structure, and magnetic properties of these species have been investigated at the density functional level. It was shown that the change of the heteroatom X via Al(III)-Si(IV)-P(V)-S(VI) slightly stabilizes the broken-symmetry (BS) state over the high-spin (HS) state, increases the antiferromagnetic coupling constant, J, of these species, and lowers the energies of their highest-occupied molecular orbitals (HOMOs) and lowest-unoccupied molecular orbitals (LUMOs). The change of the redox-active center M from Mn to Fe slightly increases the M-(XO(4)) interaction, J-coupling constant, and energy gap between the HS and BS states. Meanwhile, the LUMOs are stabilized, indicating the stronger oxidant character of [(X(n)(+)O(4))M(2)(OH)(2)W(10)O(32)]((8-n)-) for M = Fe than Mn. It was shown that the change of addenda atom M(FW) from W to Mo makes (a) the geometry of Keggin "cage" slightly smaller, (b) the interaction of redox-active centers (Fe) with the central XO(4)-unit slightly stronger, and (c) the J-coupling constant, as well as the energy gap DeltaE(BS-HS), slightly larger.