Hypersonic flows of the five-component air mixture N2/O2/NO/N/O in the relaxation zone behind shock waves are studied on the basis of the state-to-state, three-temperature and one-temperature kinetic theory approaches. The equations of non-equilibrium vibrational and chemical kinetics are coupled to the gas dynamic equations and solved numerically for Mach numbers in the free stream M = 15. The results obtained using different approaches are compared and the influence of the kinetic model on the vibrational distributions, gas temperature, velocity and mixture composition is shown.