The strengths of the bonds between the d(10) fragments M(PH3)(2) (M Ni, Pd, Pt) and the iz-ligands O-2, C2H4, and C2H2, as well as the d(8) fragments M(CO)(4) (M = Fe, Ru, Os) and ethylene, have been studied by a density functional method based on the NL-SCF+QR scheme where nonlocal (NL) and quasi-relativistic (QR) corrections are included self-consistently. All calculations are based on fully optimized geometries of the complexes and fragments involved. The calculated bond energies display a V-like trend within a triad, with a minimum at the second-row transition metal complex. This trend is largely caused by relativistic effects which become very important for the 5d elements. Without relativity the bond strengths would decrease gradually down the triad. Relativistic effects destablize the d orbitals of the third-row transition metals and hence increase the metal to ligand back-donation as well as the bond strengths. Relativistic effects are also important for the geometries of the coordinated ligands O-2. C2H4, and C2H2 Thus, the O-O or C-C bond distances are stretched and the back-bending angles in C2H4 and C2H2 increased by relativistic effects in the 5d complexes.