The roles of chemical composition (X, M and M-FW) of di-transition-metal-substituted gamma-Keggin polytungstates and polymolybdates, [(Xn+O4)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 chancre of the redox-active center M from Mn to Fe slightly increases the M-(XO4) interaction, J-coupling constant, and energy gap between the HS and BS states. Meanwhile, the LUMOs are stabilized, indicating the stronger oxidant character of [(Xn+O4)M-2(OH)(2)W10O32]((8-n)-) for M = Fe than Mn. It was shown that the change of addenda atom MFW from W to Mo makes (a) the geometry of Keggin "cage" slightly smaller, (b) the interaction of redox-active centers (Fe) with the central XO4-unit slightly stronger, and (c) the J-coupling constant, as well as the energy gap Delta E(BS-HS), slightly larger.