Investigations have been conducted to understand and experimentally validate the mechanisms of ionization in two-temperature atmospheric pressure air plasmas in which the electron temperature is elevated with respect to the gas temperature. The first part of the paper reports the results of numerical simulations performed with a new two-temperature chemical kinetic model, with reaction rate coefficients determined as weighted sums of elementary rate coefficients over the internal energy levels of atomic and molecular species. These calculations yield the surprising result that, for a given constant gas temperature, the steady-state electron number density exhibits an S-shaped dependence on the electron temperature. The middle limb of the S-shaped curve, which corresponds to electron number densities between approximately 10 13 and 10 17 e - /cm 3 , is found to be kinetically unstable. This S-shaped behavior is caused by competing ionization, charge transfer reactions, two-body dissociative recombination, and three-body electron recombination reactions, and therefore is characteristic of molecular plasmas. The numerical results are then interpreted in terms of macroscopic discharge parameters (electric field and current density) by means of Ohm's law and the electron energy equation. The resulting current density vs. electric field characteristic also exhibits an S-shaped dependence, which suggests that it may not possible to operate a stable discharge at electron number densities greater than 10 13 cm -3 by the sole use of a discharge operating at constant electric field. On the other hand, it may be possible to produce stable air plasmas by operating the electrical discharge at constant current density, as the electric field vs. current density characteristi...