A kinetic model is presented to describe the production and the growth of clusters and dust nanoparticles in low-pressure plasmas. The important processes of losses by diffusion and collisions with electrons and ions of the clusters and grains have been taken into consideration. Formulas and equations have been provided to calculate neutral and negatively charged cluster function distribution according to the number V of monomers in clusters; the critical dimension of cluster n*; the fluxes of neutral and negative clusters across point 0, which determine the rate for particle production; the density and average dimension < n > of these particles. (c) 2005 Elsevier B.V. All rights reserved.