Innermolecular motion in Na(3)AlH(6) gives rise to a Lorentzian spectrum with a wavenumber-independent width of about 1 µeV at 180 °C, which is probably due to the rotation of AlH(6) tetrahedra. There is no such quasielastic line in NaAlH(4) or NaH. Based on this finding, time-resolved measurements on the neutron backscattering spectrometer SPHERES were used to monitor the decomposition kinetics of sodium alanate, [Formula: see text] NaH. Both reaction steps were found to be accelerated by autocatalysis, most likely at the surfaces of Na(3)AlH(6) and NaH crystallites.