While describing the condensation growth of droplets in a homogeneous environment, the authors have come to the conclusion that the condensation process of vapors from small droplets onto large ones is continuously taking place, the concentration of the droplets decreasing and the average radius increasing. This process determining the evolution of aerosol, the problem is reduced to finding an asymptotic solution of a set of equations. The solutions are obtained and analyzed. The comparison of the spectra received with the experimental one shows a good qualitative agreement of the theory and the experiment.