The equilibrium structures and harmonic vibrational frequencies of peroxynitric acid (HOONO2) and seven structures of protonated peroxynitric acid, along with peroxynitrous acid (HOONO) and its 12 protonated peroxynitrous acid structures, have been investigated using several ab initio and density functional methods. The ab initio methods include second-order Møller-Plesset perturbation theory, quadratic configuration interaction, including single and double excitations theory (QCISD), and the QCISD(T) methods, which incorporate a perturbational estimate of the effects of connected triple excitation. The Becke three-parameter hybrid functional combined with Lee, Yang, and Parr correlation function is the density functional method used. The lowest energy form of protonated peroxynitric acid is a complex between H2O2 and NO+ rather than between H2O and NO2+. For peroxynitrous acid, a complex between H2O2 and NO2+ is found to be the lowest energy structure. The ab initio proton affinity (PA) of HOONO and HOONO2 is predicted to be 182.1 and 175.1 kcal mol−1, respectively, at the QCISD(T)/6-311++G(3df,3pd) level of theory. The results are contrasted with an earlier study on nitrous acid, and is shown that peroxynitric acid and peroxynitrous acid have a smaller PA than nitrous acid.