After a short discussion of the formal significance of the association parameter (A), this quantity is calculated from revised experimental results for proton magnetic relaxation rates, deuteron magnetic relaxation rates, and self-diffusion coefficients of the water in aqueous solutions of a number of 1:1 and 2:1 electrolytes. An increase of the A-parameter with decreasing water concentration, which is an indicator for water proton-proton association, was found in solutions of the structure breakers CsCl and CsBr, probably for RbCl and RbBr as well. Decrease of the A-parameter with decreasing water concentration, i.e., water deassociation, was observed for moderately hydrated cations like Li+ and Na+. In 2:1 electrolytes, partly showing complex formation, the water-water association is a more complicated function of the salt concentration.