We have studied the geometrical and electronic structure of (Al2O3)(n) (O-x) clusters with n < 15 and x=0, 1, 2 by means of first principles density functional calculations, norm-conserving pseudopotentials and a numerical atomic basis set. The equilibrium geometries have been determined by total energy minimization, starting with several initial geometries for each cluster size. The trends obtained for the atomic arrangements (structural isomers, coordination numbers, 'amorphous' vs. 'ordered' structures, etc.) and the electronic properties (binding energies, HOMO-LUMO gap, density of levels, dipole moments and Mulliken population charges) are discussed. The effect of atomic and molecular oxygen adsorption on these properties is studied.