The evolution of Titan's aerosols is studied from their production altitude down to the ground using a stochastic approach. A background aerosol distribution is assumed, obtained from previous Eulerian modelling, and the evolution of a ''tagged'' particle, released near the formation altitude, is followed by simulating in a random way its growth through coagulation with particles of the background distribution. The two distinct growth stages, proposed by Cabane et al. (1992) to explain the formation of monomers and subsequent aggregates, are confirmed. The first stage may be divided into two parts. Firstly, within ≈1 terrestrial day, particles grow mainly through collisions with larger particles. They reach their size of monomer (rm≈0.09 &mgr;m) through typically one to five such collisions. Secondly, within a few terrestrial days to ≈1 terrestrial month, particles evolve mainly by collisions with continuously created small particles and acquire their compact spherical structure. In the second stage, whose duration is ≈30 terrestrial years, or one Titan's seasonal cycle, particles grow by cluster-cluster aggregation during their fall through the atmosphere and reach, at low stratospheric levels, a typical radius of 0.4--0.5 &mgr;m. ¿ American Geophysical Union 1993