Hydrogenation reactions starting with di- or oligonuclear boron compounds featuring direct B-B bonds with the B atoms in the formal oxidation state +II are analyzed with the aid of ab initio quantum chemical (RI-MP2) calculations. The products of these reactions are B(III) hydrides which might be useful starting reagents for stoichiometric hydrogenation reactions and possibly in special cases also for hydrogen storage. Several different isomers of these B(III) hydrides featuring either terminal or bridging H atoms were considered. The results are compared to hydrogenation reactions of related molecules.