A systematic study of the dehydrogenation process of undoped and of catalyzed NaAlH4 by means of anelastic spectroscopy is presented. Evidence is reported of the formation of a highly mobile species during decomposition, which has been identified in off-stoichiometric AlH6-x units, giving rise to fast H vacancy local dynamics. The formation of such stoichiometry defects starts at temperatures much lower in Ti doped than in undoped samples, and concomitantly with the decomposition reaction. The catalyst atoms decrease the energy barrier to be overcome by H to break the bond, thus enhancing the kinetics of the chemical reactions and decreasing the temperature at which the dehydrogenation processes take place. The experimental data show that not all the hydrogen released by the formula units during the evolution of decomposition evolves out of the sample, but part of it remains in the lattice and migrates on a long-range scale within the sample. We identify, in this H mobilized population, the species which induces the fast tetragonal to monoclinic phase transformation accompanying decomposition. A partial spontaneous thermally activated regression of decomposition has also been observed by aging experiments. A model is proposed which accounts for the action of the Ti catalyst and for the atomistic mechanism of decomposition.