Electron propagator calculations provide an accurate assignment of the six lowest vertical ionization energies (IEs) of naphthalene. The first four states have pi holes and the next two have a holes. Two subsequent final states with sigma -hole and pi -hole character are close in energy. Significant shake-up character occurs in the fourth state and in the fifth pi -hole state. Computational schemes based on low-order, perturbative improvements to Koopmans's theorem results are unlikely to be valid for these two states. Assignment of the seventh and eighth states is difficult, therefore. Higher IEs are in close agreement with features seen in photoelectron spectra and in Penning ionization electron spectroscopy.