Activity and osmotic coefficients for aqueous solutions of pure nonassociating salts and their mixtures are described in the framework of the primitive model of ionic solutions in which the solvent is a dielectric continuum, using the mean spherical approximation (MSA). Expressions for these quantities are given which verify the Gibbs-Duhem relation, in the Lewis-Randall (experimental) molality scale. The model involves concentration-dependent ion size and effective permittivity. In contrast to other previous descriptions, variation of these parameters can be interpreted in terms of ionic hydration effects. The model has been applied to fit data for aqueous solutions of pure alkali halides up to very high concentrations (19 mol kg(-1) for LiCl, 20 mol kg(-1) for LiBr,...), acids such as HCl (to 16 mol kg(-1)), LiNO3, two alkali perchlorates, and uranyl perchlorate, and two-salt mixtures without a common cation. A property of the model is used to predict the behavior of two-salt mixtures with a common cation from the results for pure salt solutions. Generalization of the model to an arbitrary number of salts is tested in the case of three-salt mixtures. Generally, the calculations have been carried out up to the highest concentration for which data are available, at 25 degrees C. In all cases, the results agree with the experimental measurements to within the experimental error.