Ab initio and density functional theory (DFT) calculations with the 6-311+G(2df) basis set have been performed on Al2O3, Al2O2, and their corresponding negative ions. A triplet ground state is predicted for the Al2O3 molecule and a doublet ground state for Al2O3- Both Al2O3 and its negative ion have a C-2v structure, which is a distorted form of the structure proposed in a recent report on negative ion photoelectron spectroscopy (PES) of AlxOy- (x =1-2, y =1-5) [J. Chem. Phys. 1997, 106, 1309]. Al2O2 and its negative ion have a planar (D-2h) rhombic structure. The adiabatic electron affinity calculated at the CCSD(T) level is 3.28 eV for Al2O3 and 1.81 eV for Al2O2 compared to the experimental values of 3.71 and 1.88 eV, respectively. The singlet-triplet (S-T) gap of 0.49 eV observed for Al2O2 in the PES experiment compares quite well with our computed value of 0.47 eV. Adiabatic electron detachment energies (AEDE) of the anions calculated at the CCSD(T) level and B3LYP harmonic vibrational frequencies (including isotopic frequency shifts) of the lowest energy structures of the neutral molecules are provided for future experimental studies on these species.