We have analyzed the character of B=B and B B bonds in the neutral molecules of general form: LHB=BHL (2-L) and LB BL (3-L), for various ancillary ligands L attached to the boron center, based on a recently developed method that combines the extended transition state scheme with the theory of natural orbitals for chemical valence (ETS-NOCV). In the case of molecules with the B=B bond, 2-L, we have included L = PMe3, PF3, PCl3, PH3, C3H4N2=C(NHCH)(2), whereas for molecules containing the BB connection, 3-L, the following ligands were considered L = CO, PMe3, PCl3, (Me2NCH2CH2O)(2)Ge. The results led us to conclude that use of phosphorus ligands leads to strengthening of the B=B bond by 6.4 kcal/mol (for 2-PMe3), by 4.4 (for 2-PF3) and by 9.2 (for 2-PH3), when compared to a molecule developed on the experimental basis, 2-C3H4N2 (Delta E-total = -118.3 kcal/mol). The ETS scheme has shown that all contributions, that is, (i) orbital interaction Delta E-orb, (ii) Pauli repulsion Delta E-Pauli, and (iii) electrostatic stabilization Delta E-elstat are important in determining the trend in the B=B bond energies, Delta E-total. ETS-NOCV results revealed that both sigma(B=B) and pi(B=B) contributions are responsible for the changes in Delta E-orb values. All considered molecules of the type LB BL, 3-L, exhibit a stronger B B bond when compared to a double B=B connection in 2-L (vertical bar Delta E-total vertical bar lower by 11.8-42.5 kcal/mol, depending on the molecule). The main reason is a lower Pauli repulsion contribution noted for 3-CO, 3-PMe3, and 3-PCl3 molecules. In addition, in the case of 3-PMe3 and 3-PCl3, the orbital interaction term is more stabilizing; however, the effect is less pronounced compared to the drop in the Pauli repulsion term. In all of the systems with double and triple boron boron bonds, the electronic factor (Delta E-orb) dominates over the electrostatic contribution (Delta E-elstat). Finally, the strongest B B connection was found for 3-Ge [L = (Me2NCH2CH2O)(2)Ge], predominantly as a result of the strongest sigma- and pi-contributions, despite the highest destabilization originating from the sizable bulkiness of the germanium-containing ligand. The data on energetic stability of multiple boron boron bonds (relatively high values of bond dissociation energies vertical bar Delta E-total vertical bar), suggest that it should be possible to isolate experimentally the novel proposed systems with double BB bonds, 2-PMe3, 2-PP3, 2-PCl3, and 2-PH3, and those with triple B B connections, 3-PMe3, 3-Ge, and 3-PCl3.