A theoretical model of chemical and vibrational kinetics of hydrogen oxidation is suggested based on the consistent account for the vibrational nonequilibrium of HO2 radical which forms in result of bimolecular recombination H + O2 = HO2 in the vibrationally excited state. The chain branching H + O2 = O + OH and inhibiting H + O2 + M = HO2 + M formal reactions are considered (in the terms of elementary processes) as a general multi-channel process of forming, intramolecular energy redistribution between modes, relaxation, and monomolecular decay of the comparatively long-lived vibrationally excited HO2 radical which is capable to react and exchange of energy with another components of the mixture. The model takes into account the vibrational nonequilibrium for the starting (primary) H2 and O2 molecules, as well as the most important molecular intermediates HO2, OH, O2(1D), and the main reaction product H2O. The calculated results are compared with the shock tube experimental data for strongly diluted H2-O2 mixtures at 1000 T p < 4 atm. It is demonstrated that this approach is promising from the standpoint of reconciling the predictions of the theoretical model with experimental data obtained by different authors for various compositions and conditions using different methods. It is shown that the hydrogen-oxygen reaction proceeds in absence of vibrational equilibrium, and the vibrationally excited HO2 radical acts as a key intermediate in the principally important chain branching process. For T < 1500 K, the nature of hydrogen-oxygen reaction is especially nonequilibrium, and the vibrational nonequilibrium of HO2 radical is the essence of this process.