Dimethylamine-borane (DMAB) acid/base properties, its dihydrogen-bonded (DHB) complexes and proton transfer reaction in nonaqueous media were investigated both experimentally (IR, UV/vis, NMR, and X-ray) and theoretically (DFT, NBO, QTAIM, and NCI). The effects of DMAB concentration, solvents polarity and temperature on the degree of DMAB self-association are shown and the enthalpy of association is determined experimentally for the first time (-ΔH°assoc = 1.5-2.3 kcal/mol). The first case of "improper" (blue-shifting) NH···F hydrogen bonds was observed in fluorobenzene and perfluorobenzene solutions. It was shown that hydrogen-bonded complexes are the intermediates of proton transfer from alcohols and phenols to DMAB. The reaction mechanism was examined computationally taking into account the coordinating properties of the reaction media. The values of the rate constants of proton transfer from HFIP to DMAB in acetone were determined experimentally [(7.9 ± 0.1) × 10(-4) to (1.6 ± 0.1) × 10(-3) mol(-1)·s(-1)] at 270-310 K. Computed activation barrier of this reaction ΔG(‡theor)298 K(acetone) = 23.8 kcal/mol is in good agreement with the experimental value of the activation free energy ΔG(‡exp)270 K = 21.1 kcal/mol.