This work reviews a number of important aspects of the kinetic theory of dc ormicrowave discharge plasmas in N2, O2, H2 and their mixtures. Thefundamental problems which are addressed include (1) the determination of thenon-equilibrium electron energy distribution function from the Boltzmannequation and its coupling to the vibrational kinetics; and (2) theself-consistent modelling of such discharges taking into account bulk andsurface kinetic processes, the gas thermal balance and the charged particlebalance. In particular, the mechanisms of dissociation, ionization andproduction of H- ions are discussed. Comparisons between modelpredictions and experiment are presented.