Abstract: Hypersonic flow is usually in a thermochemical nonequilibrium state due to high temperature after the bow shock. In this paper, the state-to-state method and two-temperature models are employed to study the thermochemical nonequilibrium processes of oxygen for a post-shock flow and a flow over a blunt body along the stagnation line. The state-to-state method treats each vibrational energy level of molecular oxygen as an independent species, and predicts the number density of each vibrational level by coupling the Euler equations or reduced Navier-Stokes equations along the stagnation line. The two-temperature models assume that all vibrational levels follow the Boltzmann distribution at a vibrational temperature, and a vibrational energy equation is solved to obtain the vibrational temperature. Simulation results show that the distributions of the temperature and species concentration predicted by the state-to-state method are in good agreement with the available experimental results in the literature, while the classical two-temperature models show large errors and the results of different two-temperature models are scattered. The state-to-state method gives detailed information of all vibrational levels along the streamline. After the normal shock or bow shock, the high vibrational levels are first excited but low levels with large number density will reach thermal equilibrium first, whereas high level molecules reach thermal equilibrium only after a long distance. Near the stagnation point, the recombination reaction produces oxygen molecules that are at high vibrational levels, thus the number density of a high vibration level is significantly higher than that of the equilibrium distribution. It is also found that the dissociation rate of classical two-temperature models deviates from the state-to-state result, which cannot accurately account for the coupling effects of vibration dissociation on the dissociation rate. However, it is reasonable for Park’s two-temperature model to take the vibration energy lost by dissociation to be 0.3\sim0.5 times of the molecular dissociation energy.