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Atomic force microscopy studies of the dynamics of the nanostructure formation on a van der Waals surface of CdI2 crystals during aging in air environment under near-equilibrium thermodynamic conditions have been carried out. The nanostructure growth process is found to consist of three stages. At the first stage, there appear nano-sized pores due to the lattice dissolution at the outcrops of screw dislocations or other structural defects. At the second stage, the cone-shaped nanoclusters arise and grow in those nano-sized pores. At the third stage, the nanoclusters coagulate. The growth kinetics of cone-shaped nanoclusters is described by a diffusion model based on the interdiffusion approximation for the components. The growth rate of nanoclusters is shown to depend on the time evolution of the concentration gradient of Cd 2+ ions in the near-reaction zone. K e y w o r d s: atomic force microscopy, van der Waals surface, nanopores, nanoclusters, diffusion.