An attempt is made to assign several of the peaks observed in the anion photodetachment photoelectron spectra of Al3P- and Al3P3- reported by Gdmez, Taylor and Neumark [J. Phys. Chem. A 2001, 105, 6886]. For the Al3P/Al3P- system, equilibrium geometries and harmonic vibrational frequencies are computed for several low-lying electronic states of the neutral molecule and the anion at the B3LYP, MP2, and CCSD(T) levels of theory using the 6-311+G(2df) one-particle basis set. Al3P- has a B-2(2) (C-2nu) ground state, whereas a near degeneracy is found between the (1)A(1) (C-3nu) and (1)A(1) (C-2nu) states of the Al3P molecule. The assignment of the Al3P- electron detachment spectrum is based on transitions from the B-2(2) (C-2nu) ground state of the anion to neutral states with the same C-2nu geometry. On the other hand, the adiabatic electron affinity (AEA) of Al3P is computed as the difference in the total energies of the 2132 (C-2nu) ground state of the anion and the (1)A(1) (C-3nu) ground state of the neutral. Its value is 1.76 eV at the CCSD(T) level. A value of 2.051 +/- 0.020 eV reported as the AEA of Al3P in the photoelectron study is assigned to the energy difference between the zero point vibrational levels of the 2132 (C-2nu) state of the anion and (1)A(1) (C(2)nu) state of the neutral. In the case of the Al3P3-/Al3P3 system, the smallest basis set used is 6-311+G(d) and the largest is 6-311+G(3df). The anion has a (2)A'(1) (D-3h) ground state that is well separated from other states, whereas, the (1)A'(1) (D-3h) and the (1)A' (C-s) states of the neutral have almost the same energy. Vertical electron detachment energies (VEDE) computed for transitions originating from the (2)A'(1) ground state of the anion to neutral states with the D-3h geometry are in very good agreement with the experimental photoelectron data. Assuming a (1)A'(1) (D-3h) ground state, the AEA of Al3P3 is computed to be 2.39 eV at the CCSD(T) level. For a (1)A' (C-s) ground state, a value of 2.46 eV is obtained at the same level of theory. The experimental AEA of Al3P3 obtained from the photoelectron study is 2.450 +/- 0.020 eV.