The structural and electronic properties of Al m H n clusters have been studied employing the density functional formalism. Addition of hydrogen only affects the structure of the Al matrix in a minor way, except in the series Al 4 H n and Al 5 H n . The binding energies per atom increase fast with the addition of H atoms to the bare Al m cluster, reflecting a strong Al-H bonding, but as the H coverage becomes substantial the binding energies per atom tend to a constant value. Two measures of the cluster stability have been analyzed: the first is a stability function comparing the energy of the cluster Al m H n to the average of the energies of clusters Al m H n−1 and Al m H n+1 , and the second is the chemical hardness K . Those two quantities, which show a perfect correlation, display an alternating behavior of large and small values in series Al m H n with constant m and varying n. This trend is associated to the alternation of odd and even number of electrons as n increases in each series. The ionization potential and the electron affinity also show an odd-even alternation in many of the series with a common m, but the exceptions are frequent.