The application of the Monte Carlo (MC) simulation technique for the modelling of nucleation processes with an existing background particle concentration is presented in this paper. Next to the nucleation of novel particles, the coagulation of an existing particle population as well as the condensational growth and evaporation of unstable particles (whose diameter is smaller than the critical Kelvin diameter) are included into the simulation. The usage of statistically weighted MC particles allows the description of particle size distribution (PSD), whose concentrations differ in several orders of magnitude. It is shown, that this approach allows to model the complex interplay between freshly nucleated particles and an existing background particle population. In this work, the nucleation of novel particles is modelled by three different nucleation theories discussed by [Girshick, S. L. and C.-P. Chiu (1990), The Journal of Chemical Physics 93], which comprise of (1) the classical nucleation theory, (2) a mathematical correction to (1) and (3) a self-consistency correction of (2). For the chosen simulation conditions, the resulting PSDs are independent of the used nucleation theory for longer simulation times, in which the simulations are described by the coagulation mechanism only. The time-frame is identified for which relevant discrepancies of the PSDs have to be taken into account.