The bonding situation of homonuclear and heteronuclear metal-metal multiple bonds in R3M-M'R-3 (M, M' = Cr, Mo, W; R = Cl, NMe2) is investigated by density functional theory (DFT) calculations, with the help of energy decomposition analysis (EDA). The M-M' bond strength increases as M and M' become heavier. The strongest bond is predicted for the 5d-5d tungsten complexes (NMe2)(3)W-W(NMe2)(3) (D-e = 103.6 kcal/mol) and Cl3W-WCl3 (D-e = 99.8 kcal/mol). Although the heteronuclear molecules with polar M-M' bonds are not known experimentally, the predicted bond dissociation energies of up to 94.1 kcal/mol for (NMe2)(3)Mo-W(NMe2)(3) indicate that they are stable enough to be isolated in the condensed phase. The results of the EDA show that the stronger R3M-M'R-3 bonds for heavier metal atoms can be ascribed to the larger electrostatic interaction caused by effective attraction between the expanding valence orbitals in one metal atom and the more positively charged nucleus in the other metal atom. The orbital interaction reveal that the covalency of the homonuclear and heteronuclear R3M-M'R-3 bonds is due to genuine triple bonds with one sigma- and one degenerate pi-symmetric component. The metal-metal bonds may be classified as triple bonds where pi-bonding is much stronger than sigma-bonding; however, the largest attraction comes from the quasiclassical contribution to the metal-metal bonding. The heterodimetallic species show only moderate polarity and their properties and stabilities are intermediate between the corresponding homodimetallic species, a fact which should allow for the experimental isolation of heterodinuclear species. CASPT2 calculations of Cl3M-MCl3 (M = Cr, Mo, W) support the assignment of the molecules as triply bonded systems.