The low-lying electronic states of Al3As, AlAs3, and the corresponding anions have been studied at the B3LYP and CCSD(T) levels using the 6-311+G(2df) one-particle basis set. The ground electronic states of Al3As- and Al3As have a cyclic planar C-2nu geometry. A (1)A(1)-(C-3nu) state is located 0.2 eV above the (1)A(1)-(C-2nu) ground state of Al3As. For AlAs3, a near degeneracy is found between the (1)A(1) (C-2nu) and the (1)A' (C-s) lowest states while the anion, AlAs-, has a (2)A' (C-s) ground state. The adiabatic electron affinities of Al3As and AlAs3 are calculated to be 1.8 and 1.9 eV, respectively. Electron detachment energies computed for the anions and the harmonic vibrational frequencies of both the anions and the neutral molecules are presented and discussed. It is anticipated that the computed data will aid future analysis and the interpretation of experimental photoelectron photodetachment spectra of these systems.