State-to-state and two-temperature theoretical models for high-temperature strongly nonequilibrium reacting air flows and heat and radiative fluxes are developed in the framework of the generalized Chapman–Enskog method. In the theoretical approach, systems of governing equations for coupled fluid dynamics, chemical kinetics, internal energy transitions and radiation are derived; algorithms for calculating the state-to-state transport coefficients are developed and implemented. The proposed models are applied for simulations of planar shock waves in air under high-temperature conditions observed in flight experiments. A nonequilibrium mixture composition, temperatures and pressure profiles are obtained. We demonstrate that flow variables strongly depend on both the applied approach of kinetic theory and choice of the chemical-reaction model: species molar fractions and temperature show significantly different behaviors for the state-to-state and two-temperature simulations. The transport properties and radiative fluxes are calculated as functions of the distance from the shock front. It is found that diffusion provides a major contribution to the total energy flux whereas the role of heat conduction is weak due to compensation effects. We show that under the considered conditions, two-temperature models are not applicable for correct predictions of radiative heating.