The geometries and the bonding properties have been predicted for cyclic AlO2 and AlS2 species in doublet and quartet states using density functional theory, the second, third, and fourth orders Moller-Plesset theory, quadric configuration interaction singles and doubles including a perturbational estimate of the triples and coupled cluster singles and doubles including a perturbational estimate of the triples all-electron correlation methods with 6-311+G* and aug-cc-pvtz basis sets. The geometrical optimizations and the harmonic vibrational frequency analysis are performed using density functional theory and coupled cluster singles and doubles methods. The relevant energy quantities are also determined using several high-order electron correlation methods (the second, third, and fourth orders Moller-Plesset theory, quadric configuration interaction, and coupled cluster theories) at both basis set levels (6-311+G* and aug-cc-pvtz). For the doublet state, each species possesses a (2)A(2) ground state with a higher energy level (2)A(1) state. The corresponding state-state separations are 11 kcal/mol for AlO2 species and 7.2 kcal/mol for AlS2 species at coupled cluster singles and doubles including a perturbational estimate of the triples and 6-311+G* level. The calculations using quadric configuration interaction and coupled cluster singles and doubles including a perturbational estimate of the triples yield dissociation energies in three dissociation mechanisms of similar to 59, similar to 190, and similar to 294 kcal/mol for AlO2((2)A(2)), and of similar to 64, similar to 167, and similar to 272 kcal/mol for AlS2((2)A(2)), respectively, and other methods [B3LYP, B3P86, B3PW91, Moller-Plesset (n=2,3,4), quadric configuration interaction and coupled cluster singles and doubles] yield dissociation energies within similar to 4.5 kcal/mol. For the quartet states, the B-4(1) state is more stable than the B-4(2) state with energy separations of 43.5 kcal/mol for AlO2 and 29 kcal/mol for AlS2. The B-4(1) and B-4(2) states are significantly higher in energy than the ground states by 28.9 kcal/mol (B-4(1)) and 57.9 kcal/mol (B-4(2)) for AlS2, and 24.2 kcal/mol (B-4(1)), and 67.8 kcal/mol (B-4(2)) for AlO2. Result analysis has indicated that the cyclic AlO2 in the (2)A(2) and B-4(2) states should be classified as superoxides, but they have different spin density distribution. However, AlO2 in the (2)A(1) state should not be, while AlO2 in the B-4(1) state may be classified as the dioxide. The AlS2 species in the (2)A(2) state should be classified as a supersulfide. Although the (2)A(1) state has some supersulfide character, it should not be classified as such. The AlS2 in the B-4(2) and B-4(1) states should be classified as the weak interaction molecular complex and the disulfides, respectively. However, these superoxides and supersulfides are far less ionic than the corresponding alkali metal superoxides.