Density functional theory with nonlocal corrections (Becke3LYP) and Hartree-Fock theory with perturbative electron correlation (QCISD(T)) are used to study the nitrogen oxides. With few exceptions, DFT calculations With a small basis set (6-31G(d)) are in good agreement with QCISD(T) calculations with a moderate basis set (6-31+G-(2df)). A new isomer of N2O4 is calculated which involves the coupling of two NO2 radicals through oxygens. The O-O bond in ONOONO is similar to other peroxide bonds except that the bond dissociation energy is negative (-17.5 kcal/mol) due to the large reorganization energy of NO2. The ONOONO intermediate is suggested to play a key role in the reaction 2NO + O-2 --> 2NO(2). The stepwise mechanism for formation of ONOONO, adding NO to O-2 (endothermic by 11.5 kcal/mol) followed by adding NO to ONOO (exothermic by 21.6 kcal/mol), is not consistent with experimental observations. Rather, a new mechanism is proposed in which ONOONO is formed in a concerted step from NO plus NO.O-2, a weakly bound complex of NO and O-2. Assuming O-O cleavage as the rate determining step gives the correct rate law ([O-2][NO](2)) and an overall activation barrier consistent with experiment.