The results of a numerical study of kinetic processes initiated by pulsed nanosecond discharge in atmospheric-pressure air are presented. The calculations of temporal dynamics of electron concentration, density of atomic oxygen, vibrational distribution function of nitrogen molecules, and gas temperature agree with the experimental data. It was shown that quenching of electronically excited states of nitrogen N 2 (B 3 П g ), N 2 (С 3 П u ), N 2 (a' 1 u ) by oxygen molecules leads to the dissociation of O 2 . This conclusion is based on the comparison of calculated dynamics of atomic oxygen in air, excited by pulsed nanosecond discharge, with experimental data.In air plasma at high dissociation degree of oxygen molecules, relaxation of electronic energy of atoms and molecules in reactions with O atoms becomes extremely important. Active production of NO molecules and fast gas heating in the discharge plasma due to the quenching of electronically excited N 2 (B 3 П g , C 3 П u , a' 1 u ) molecules by oxygen atoms should be noted here. Owing to the high O atoms density, negative ions are efficiently destroyed in the discharge afterglow. As a result, the decay of plasma in the afterglow is determined by electron-ion and ion-ion recombination, and the electron density in the region of high Oatoms density remains relatively high between the pulses. This is the reason why the next pulse does not lead to the streamer formation, but instead the Townsend mechanism of the discharge is initiated. An increase of vibrational temperature of nitrogen molecules at the periphery of plasma channel at time delay t = 1 -30 s after the discharge was obtained. This is due to the intense gas heating and as a result, gas-dynamic expansion of a hot gas channel. Vibrationally excited N 2 (v) molecules produced near the discharge axis moves from the axial region to the periphery. Consequently, at the periphery the vibrational temperature of nitrogen molecules is increased.