The peroxy isomers of nitrate and nitric acid, peroxynitrite and peroxynitrous acid, are studied with ab initio and density functional methods. The results are compared to the observed Raman and 15N NMR spectra. The harmonic vibrational frequencies, NMR chemical shifts, and energies clearly favor cis ONOO- as the most stable and predominant ONOO- isomer. Peroxynitrite has a large rotational barrier of ∼24 kcal/mol because of partial π-bonding in the central bond. This is confirmed by a bond order of 1.5 for cis and trans ONOO- computed by electron density analysis. Electron correlation is critical in accurately predicting the relative energies for this system, as Hartree-Fock predicts a lower triplet state. The intense, broad band in the solution Raman spectrum centered at 642 cm-1 is predicted to be too low by 100-150 cm-1 if the vibration is the cis torsion. Resolution of this discrepancy is attempted by estimating the effects of solvent and anharmonicity. The results on ONOO- are compared to those for ONOOH, which is adequately described by lower levels of theory. The planar cis-cis isomer of ONOOH is the lowest energy structure by 1-2 kcal/mol.