A theoretical model is proposed for the chemical and vibrational kinetics of hydrogen oxidation based on consistent accounting of the vibrational non-equilibrium of the HO2 radical that forms as a result of the bimolecular recombination H+O2 → HO2. In the proposed model, the chain branching H+O2 = O+OH and inhibiting H+O2+M = HO2+M formal reactions are treated (in the terms of elementary processes) as a single multi-channel process of forming, intramolecular energy redistribution between modes, relaxation, and unimolecular decay of the comparatively long-lived vibrationally excited HO2 radical, which is able to react and exchange energy with the other components of the mixture. The model takes into account the vibrational non-equilibrium of the starting (primary) H2 and O2 molecules, as well as the most important molecular intermediates HO2, OH, O2(1Δ), and the main reaction product H2O. It is shown that the hydrogen–oxygen reaction proceeds in the absence of vibrational equilibrium, and the vibrationally excited HO2(v) radical acts as a key intermediate in a fundamentally important chain branching process and in the generation of electronically excited species O2(1Δ), O(1D), and OH(2Σ+). The calculated results are compared with the shock tube experimental data for strongly diluted H2–O2 mixtures at 1000 < T < 2500 K, 0.5 < 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. For T < 1500 K, the nature of the hydrogen–oxygen reaction is especially non-equilibrium, and the vibrational non-equilibrium of the HO2 radical is the essence of this process. The quantitative estimation of the vibrational relaxation characteristic time of the HO2 radical in its collisions with H2 molecules has been obtained as a result of the comparison of different experimental data on induction time measurements with the relevant calculations.