In the present study, three different electronic state-to-state methods are proposed to analyze nonequilibrium air plasma flows behind a strong shock wave. In the first approach representing the conventional method, a two-temperature model combined with the electronic quasi-steady-state assumption is adopted. In the second and the third methods, atomic and molecular electronic master equations are coupled with a conservation equation to describe the electronic state-to-state kinetics. State-of-the-art electronic transition rates for atmospheric gas species are compiled with comparisons of existing data. A prediction of the measured nonequilibrium radiation is made for the flow conditions of recent electric-arc shock tube experiments. In a comparison with the measured spectrum, the present electronic master equation coupling methods are more accurate than the conventional approach when used to estimate the initial rising rate and peak value of the diatomic intensity and small amounts of atomic radiation when the diatomic nonequilibrium condition is dominant. Moreover, the spatial distributions of the intensity and electron number density are more accurately predicted by the present methods when the flow fields are dominated by atomic nonequilibrium.