Non-equilibrium reaction rates in the 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. State-dependent rate coefficients for N2 and O2 dissociation and Zeldovich exchange reactions are averaged using 1) state-to-state vibrational distributions, 2) two-temperature Treanor distributions and 3) thermal equilibrium distributions. Variation of global reaction rate coefficients obtained in different approaches along the relaxation zone is studied numerically for free stream Mach number M = 13 and differences between reaction rate coefficients found in the frame of the state-to-state and more simple kinetic models are evaluated.