A nonlinear time-dependent two-temperature collisional-radiative model for air plasma has been developed for pressures between 1 kPa and atmospheric pressure to be applied to the flow conditions of space vehicle re-entry into the Earth's atmosphere. The model consists of 13 species: N-2, O-2, N, O, NO, N-2(+), O-2(+), N+, O+, NO+, O-2(-), O- in their ground state and major electronic excited states and of electrons. Many elementary processes are considered given the temperatures involved (up to 10 000 K). Time scales to reach the final nonequilibrium or equilibrium steady states are derived. Then we apply our model to two typical re-entry situations and show that O-2(-) and O- play an important role during the ionization phase. Finally, a comparison with existing reduced kinetic mechanisms puts forward significant discrepancies for high velocity flows when the flow is in chemical nonequilibrium and smaller discrepancies when the flow is close to chemical equilibrium. This comparison illustrates the interest of using a time-dependent collisional-radiative model to validate reduced kinetic schemes for the relevant time scales of the flows studied.