A one-dimensional transient mathematical model is used for the study of the salt diffusion and stability of the density gradient in a solar pond. A finite difference method with a diffusion coefficient dependent on both temperature and salt concentration is used to solve the salt diffusion equation. On the basis of simple considerations we analyze the influence of the salinity-gradient thickness on the useful energy which can be withdrawn from the bottom layer of the solar pond. Finally some considerations on the effect of the velocity of injected brine in rising solar ponds are presented, making use of the Rayleigh analysis of the small perturbations in order to study the stability of the system. (C) 2003 Elsevier Ltd. All rights reserved.