A combined model of the atmosphere hydrothermodynamics and the pollutant transport is described. The atmospheric pollution processes are considered having regard to the aerosol coagulation. The coagulation is allowed for by the Smolukhovsky equation. To transform the equation into the form solvable numerically, we divide the mass range of particles involved in coagulation into fractions on a logarithmic scale. This allows us to describe a wide range of masses by using a small number of equations without any loss in accuracy. The coagulation kernels are taken close to reality, which allows us to take into consideration the change-over from one collision regime to another (free molecular, transition and diffuse regimes). Implementation of the numerical model and discussion of numerical experiments are presented as well.The atmospheric aerosols (small particles suspended in the air) were known for more than a hundred years, but only in the last decade their role in global atmospheric processes stimulated their thorough investigation. By now the atmospheric aerosols are known to affect the weather and climate on our planet, the radiation and energy balances of the atmosphere, the precipitation and cloud formation processes.Though the natural aerosols account for about 90% of the total aerosol mass, the important role of the anthropogenic aerosols becomes more and more clear, since the remaining 10% of the anthropogenic aerosols possesses anomalous physical and chemical properties and can induce and transform many chemical processes in the atmosphere. On the one hand, these processes supply the atmosphere with contaminations causing smog, global geophysical phenomena, acid rains, elc., on the other hand, they can provide efficient mechanisms for removing the anthropogenic pollution from the atmosphere.As a rule, the atmospheric pollutants are polydispersive, hence to model their dynamics numerically one needs to consider two main mechanisms: (1) the transport and diffusion of pollutants and (2) the changes of the aerosol concentration and disperse composition due to such kinetic processes as condensation, coagulation, nucleation, precipitation, etc. As these processes take place in the turbulent atmosphere, the problem of the aerosol dynamics must be solved using the hydrodynamic models. This allows one to reproduce the space and temporal variations in the fields of meteoelements and in the turbulent characteristics of the atmosphere.Some physical mechanisms of the aerosol formation are being intensively investigated in recent years. A wide range of problems is discussed in the Proceedings of the International Conference on Atmospheric Aerosols [2]. However, these papers are practically devoid of complex models which simultaneously allow for the aerosol transfer, transformation, origin and destruction processes taking place in the conditions of the atmospheric circulation. It is obvious that nowadays the development of such models is of great importance, since they allow one to describe precisely the aerosol dynamics ...