The oxidative addition of pi- and sigma-bonds is studied by means of quantum chemical investigations at a MCSCF and density functional level of sophistication. The title compound (AlNacNac) induces first-order strong donor-acceptor abilities in the triplet state, giving rise to biradicaloid adducts. At second-order, it reveals carbene character. The energy barriers for the 1,2-addition reactions are fairly small, resulting from an oxidative addition, which differs from the classical 1,2-addition reaction of a carbene to an olefin. For the splitting of sigma-bonds (H-X) the energy barriers are largely driven by the strengths of the H-X bonds. The metal Al increases continuously its oxidation state from the educt over the transition state to the product. This implies that in the latter complexes the metal is positive and the olefin overall negative in charge. Ethylene itself does not form a stable adduct; it is still in equilibrium with AlNacNac plus ethylene. However, electron releasing substituents stabilize the addition product. The stabilities of various three-membered ring systems are evaluated. Hydrogen splitting possesses a relatively large barrier.