This book reviews the approach to the kinetic simulation of nonequilib rium processes in the planetary atmospheres which the authors developed and dealt with since the 1970s. The results of this study, which are focused on the nonequilibrium collisional processes in the atmospheres of planets and comets, are thoroughly reviewed and discussed. Many specific problems of atmospheric modeling, involving numerical evaluation of aeronomic pro cesses, are addressed and compared with the available experimental data. The kinetic approach proved to be especially effective to model the in teraction of the incident shortwave solar radiation with the rarefied gas of planetary upper atmospheres. It involves various processes of photolysis, en ergetic electron impacts, and accompanying numerous chemical reactions, as well as processes occurring in the intermediate ( transition ) zones of planetary and cometary gas envelopes. The underlying mathematical treat ment is based on the stochastic approach for the solution of the Boltzmann type equation and implies the development of the efficient algorithms for its computer simulation. Some results of this study were previously summa rized in the monograph issued in Russian (Marov et al. , 1990) and later in the review paper published in Space Science Reviews (Marov et al. , 1996). The basic principles of stochastic simulation were first developed in the field of rarefied gas dynamics and were successfully applied to the solution of some engineering problems of aerodynamics and heat transfer.