Quantum-chemical calculations using DFT (BP86) and ab initio methods (MP2, SCS-MP2) have been carried out for the endohedral fullerenes Ng2@C60 (Ng=He–Xe). The nature of the interactions has been analyzed with charge- and energy-partitioning methods and with the topological analysis of the electron density (Atoms-in-Molecules (AIM)). The calculations predict that the equilibrium geometries of Ng2@C60 have D3d symmetry when Ng=Ne, Ar, Kr, while the energy-minimum structure of Xe2@C60 has D5d symmetry. The precession movement of He2 in He2@C60 has practically no barrier. The NgNg distances in Ng2@C60 are much shorter than in free Ng2. All compounds Ng2@C60 are thermodynamically unstable towards loss of the noble gas atoms. The heavier species Ar2@C60, Kr2@C60, and Xe2@C60 are high energy compounds which are at the BSSE corrected SCS-MP2/TZVPP level in the range 96.7–305.5 kcal mol−1 less stable than free C60 + 2 Ng. The AIM method reveals that there is always an NgNg bond path in Ng2@C60. There are six NgC bond paths in (D3d) Ar2@C60, Kr2@C60, and Xe2@C60, whereas the lighter D3d homologues He2@C60 and Ne2@C60 have only three NgC2 paths. The calculated charge distribution and the orbital analysis clearly show that the bonding situation in Xe2@C60 significantly differs from those of the lighter homologues. The atomic partial charge of the [Xe2] moiety is +1.06, whereas the charges of the lighter dimers [Ng2] are close to zero. The a2u HOMO of (D3d) Xe2@C60 in the 1A1g state shows a large mixing of the highest lying occupied σ* orbital of [Xe2] and the orbitals of the C60 cage. There is only a small gap between the a2u HOMO of Xe2@C60 and the eu LUMO and the a2u LUMO+1. The calculations show that there are several triplet states which are close in energy to each other and to the 1A1g state. The bonding analysis suggests that the interacting species in Xe2@C60 are the charged species Xe2q+ and C60q−, where 1<q<2. The calculated XeXe distance in the endohedral fullerene (2.494 Å) is even shorter than the calculated value for free Xe22+ (2.746 Å). Thus, the XeC and XeXe interactions in Xe2@C60 should be considered as genuine chemical bonds which are enforced by the compression energy. The NgNg and NgC interactions in the lighter homologues Ar2@C60 and Kr2@C60 may also be considered as chemical bonds because the theoretically predicted properties of the endohedral fullerenes are significantly different from the free C60 and noble gas atoms. According to the bonding analysis, He2@C60 and Ne2@C60 are weakly bonded van der Waals complexes.