Dinuclear eta(2),mu(2)-bonded amidinate complexes to group 13 element hydrides are of potential interest for applications in the field of hydrogen storage. In this work repeated dihydrogen elimination starting with amidine-stabilized boron, aluminum, and gallium hydrides is discussed on the basis of quantum chemical calculations which give useful information about the thermodynamic properties of these reactions and the possible reaction pathways in dependence of the chosen amidine derivative. It will be shown that, in agreement to recent experimental work, the thermodynamic properties are greatly influenced by the nature of the substituents bonded to the amidine. The amidine stabilized hydrides first eliminate dihydrogen in an intramolecular process leading to mononuclear amidinate complexes. These complexes could dimerize, if the amidine carries not too bulky organic groups, to give dinuclear complexes featuring two eta(2),mu(2)-coordinated amidinate ligands. Further dihydrogen elimination leads to the generation of a dinuclear species with two group 13 elements (E) in the formal oxidation state +II and direct E-E bonding. Finally, elimination of another H-2 for E = B possibly gives amidinate complexes featuring a double bond between two boron atoms in the formal oxidation state +I.