Electron propagator calculations in two approximations the third-order algebraic, diagrammatic construction and the outer valence Green's function (OVGF) have been performed on the vertical electron affinities of C-60 and the vertical electron detachment energies of several states of C-60(-) with a variety of basis sets. These calculations predict bound T-2(1u) and T-2(1g) anions, but fail to produce T-2(2u) or H-2(g) anionic states that are more stable than ground-state C-60. The electron affinity for the (2)A(g) state is close to zero, but no definitive result on its sign has been obtained. This state may be a resonance or marginally bound anion. The OVGF prediction for the vertical electron detachment energy of T-2(1u) Ca-60(-) 2.63 eV, is in excellent agreement with recent anion photoelectron spectra.