Proton-transter and H-2-elimination reactions of aluminum hydride AlH3(NMe3) (TMAA) with XH acids were studied by means of IR and NMR spectroscopy and DFT calculations. The dihydrogen-bonded (DHB) intermediates in the interaction of the TMAA with XH acids (CH3OH, (PrOH)-Pr-i, CF3CH2OH, adamantyl acetylene, indole, 2,3,4,5,6-pentafluoroaniline, and 2,3,5,6-tetrachloroaniline) were examined experimentally at low temperatures, and the spectroscopic characteristics, dihydrogen bond strength and structures, and the electronic and energetic characteristics of these complexes were determined by combining experimental and theoretical approaches. The possibility of two different types of DHB complexes with polydentate proton donors (typical monodentate and bidentate coordination with the formation of a symmetrical chelate structure) was shown by DFT calculations and was experimentally proven in solution. The DHB complexes are intermediates of proton-transfer and H-2-elimination reactions. The extent of this reaction is very dependent on the acid strength and temperature. With temperature increases the elimination of H-2 was observed for OH and NH acids, yielding the reaction products with Al-O and Al-N bonds. The reaction mechanism was computationally studied. Besides the DHB pathway for proton transfer, another pathway starting from a Lewis complex was discovered. Preference for one of the pathways is related to the acid strength and the nucleophilicity of the proton donor. As a consequence of the dual Lewis acid-base nature of neutral aluminum hydride, participation of a second ROH molecule acting as a bifunctional catalyst forming a six-member cycle connecting aluminum and hydride sites notably reduces the reaction barrier. This mechanism could operate for proton transfer from weak OH acids to TMAA in the presence of an excess of proton donor.