The vibrational properties of the recently discovered aluminum hydrides SrAl2H2 and SrAISH have been investigated by means of inelastic neutron scattering (INS) and first-principles calculations. Both compounds contain AI-H units being part of a two-dimensional polyanionic layer, [(AIH)(AIH)](2-) and [Si(AIH)](2-), respectively. The INS spectrum of SrAISH is characterized by very weakly dispersed AI-H modes with well-resolved overtones, while SrA12H2 yields a solid-state dispersed phonon spectrum. The frequency of the stretching mode of the AI-H unit in SrAISH is the hitherto lowest observed for a terminal AI-H bond. At the same time, SrAISH displays the highest decomposition temperature known for an aluminum hydride compound. It is proposed that the stability of solid-state aluminum hydrides correlates inversely with the strength of AI-H bonding.