Condensational growth of foreign aerosol particles in the presence of a spacially uniform source of condensable vapour is considered assuming the latter to be able to produce new particles by nucleation. These newly born particles, in turn, grow by condensation and coagulate depositing simultaneously onto the foreign particles surfaces. A model of this process is proposed. Two new approximations are introduced allowing for a simple description of free molecular and transition regimes of the condensational process in terms of the generalised moments of the foreign particle size distribution, with no assumptions being done on the shape of the latter. The behaviour of the nucleation mode is considered within a lognormal theory that describes the evolution of the size spectrum in terms of a lognormal distribution with time-dependent parameters (the total mass, number concentration and the width of the distribution). The set of six ordinary first-order differential equations is formulated for the time dependencies of the vapour concentration, mass and number concentrations of the nucleation mode, the width of the lognormal distribution of the nucleation mode and two generalised moments of the foreign particle size distributions. Final results are presented as the products of nondimensional functions by the dimensional carriers expressed in terms of the external parameters: the number concentration of foreign aerosol N-f0 and the vapour source productivity I. Numerical calculations are performed for normal atmospheric conditions in rural areas (the source productivity does not exceed 10(7) molecules cm(-3) and the concentration of foreign particles is less than 10(3) particles cm-3) and assuming that the nonbarrier nucleation (dimers are stable) produces the particles of nucleation mode. The time dependencies of all values of interest are plotted and discussed in view of the correspondence of the model to the atmospheric reality. Only one nondimensional group gamma proportional to I/N-f0(2) governs the dynamics of the particle formation-growth process. It is shown that the maximal number concentration of newly born particles decreases in increasing the number concentration of foreign particles. This dependence displays an unexpected discontinuity (a first-order phase transition): at a critical value of the governing parameter the intensity of the nucleation burst changes by about two decimal orders. (C) 2000 Elsevier Science Ltd. All rights reserved.