A numerical model that simulates groundwater flow and solute transport for cases in which fluid properties are variable was applied in one dimension (vertical) to the shallow, low-permeability, clayey, confining layer in Do¿ana National Park in southwestern Spain. The salinity in the 80-m-thick confining layer decreases from a brine near the land surface to fresh water near its base. Results of model simulations indicate that the system could be in or close to a steady state condition. The model calibration was very sensitive to small variations in individual model parameters and was nonunique in the sense that equally good calibrations could be achieved by compensatory joint perturbations in the permeability, diffusion coefficient, and overall governing hydraulic gradient. At present, there is probably an upward flow of the order of 1 mm yr-1 to 1 cm yr-1 and a balance in the solute flux between upward advection and downward diffusion. The time scale of calculated responses to changes in boundary conditions in this low-permeability system ranges from thousands to hundreds of thousands of years when considering extremes within the range of uncertainty of values of the evaluated parameters. ¿ American Geophysical Union 1993