An investigation is made of the evolution of the size distribution of nuclei at successive moments during the condensation of Au on KCl at various temperatures. It is shown that during the earlier stage, which can be recorded with an electron microscope, there is a very narrow distribution which is approximated satisfactorily by the lognormal law. The nature of the subsequent evolution depends on the substrate temperature. At low temperatures (T less than equivalent to 250 degree C), beginning from a certain moment, a bimodal distribution is formed: its principal maximum is lognormal and a secondary maximum appears in the small-size range because of the continuing nucleation. At high temperatures (T similar 400 degree C) the distribution remains unimodal throughout the investigated condensation processes because the mobility of the nuclei is such that the rate of nucleation is far too low for the formation of a secondary maximum although it is sufficient to produce a tail extending in the direction of smaller sizes. It has been established that the variance of the logarithm of the size ( sigma **2) is almost constant during the condensation process, remaining within the limits sigma approximately equals 0. 1-0. 2, so that a two-parameter lognormal distribution becomes in fact a function of a single parameter mu ( equals InR). It is shown that a gamma distribution, more convenient in theoretical calculations, also describes well the observed size distribution of the nuclei.