The time-dependent change in particle size distributions of highly concentrated polydisperse aerosols undergoing Brownian coagulation was studied by numerically solving the basic equation of coagulation for various size distributions initially having log-normal form. The results were plotted in the forms of the change with time in cumulative size distributions and the changes in nominal geometric mean radius, as well as standard deviation for various initial distributions of aerosols. These figures showed that size distributions approached certain asymptotic ones, which might correspond to SPDF (self-preserving distribution function), almost independently of initial distributions as coagulation proceeded. The process of the approach to asymptotic distributions was also made clear by the graphs. Some of these results were verified by experimental results obtained by the ultramicroscopic size analysis previously developed by the authors.