The charge distribution on polydispersed aerosol particles was obtained by a simultaneous solution of the ion-aerosol balance equations for a finite range of aerosol sizes. All aerosols were assumed to be uncharged initially, and external electric fields, particle transport, coagulation and turbulence were ignored. The effects of varying the aerosol size distribution, aerosol concentration, and initial positive space charge on the charging process were considered for particles between 0.01- and 0.5- μm radius. Results show that a larger depletion in the free negative ion concentration occurred early in the charging process due to the larger values of the attachment coefficients of negative ions to aerosols. It was found that for small aerosol concentrations, particles were charged mostly negatively, but that an increase in aerosol concentrations lead to differential charging, resulting in opposite charging of the small (mostly negative) and the large (mostly positive) particles. This effect was enhanced for size distributions which had a significant component of large particles. The time needed for a polydispersed aerosol to reach steady state is long and grows with particle concentration. ¿ American Geophysical Union 1989