System for supplying and treating water for a washing machine, in particular a dishwasher, comprising: - a first tank for containing substances with water-softening properties, having at least one inlet opening for water to be softened and an outlet opening for softened water, - a second salt-containing tank, having at least one water inlet opening and an outlet opening for a regenerating brine formed following the dissolution of the salt in the water, - a line connecting the second tank to the first tank for the outflow of the brine formed in the second tank towards the first tank, - a water supply line having a branch-off point into a first branch supplying the first tank and into a second branch which leads to the inlet opening of the second tank, - first electric valve means adapted to control the flow of water through said supply line, - second electric valve means adapted to control a flow of water towards and through the second tank for forming the regenerating brine, - means for determining the amounts of water used for washing the dishes, forming the regenerating brine and washing the softening substances after a regenerating operation; and - electronic control means connected to said determining means and to said first and second electric valve means (12, 38); the system being characterized in that said system further comprises indicator means adapted to provide signals or data indicative of the hardness of the water used, and in that the control means are designed to control, and if necessary selectively vary, in predetermined ways, as a function of the water hardness indicated by the indicator means, and through said first and second electric valve means (12, 38): * the quantity of water used for forming the brine used for each operation of regenerating the softening substances contained in said first tank, and * the frequency of the operations of regenerating and washing said softening substances. - a first tank for containing substances with water-softening properties, having at least one inlet opening for water to be softened and an outlet opening for softened water, - a second salt-containing tank, having at least one water inlet opening and an outlet opening for a regenerating brine formed following the dissolution of the salt in the water, - a line connecting the second tank to the first tank for the outflow of the brine formed in the second tank towards the first tank, - a water supply line having a branch-off point into a first branch supplying the first tank and into a second branch which leads to the inlet opening of the second tank, - first electric valve means adapted to control the flow of water through said supply line, - second electric valve means adapted to control a flow of water towards and through the second tank for forming the regenerating brine, - means for determining the amounts of water used for washing the dishes, forming the regenerating brine and washing the softening substances after a regenerating operation; and - electronic control means connected to said determining means and to said first and second electric valve means (12, 38); the system being characterized in that said system further comprises indicator means adapted to provide signals or data indicative of the hardness of the water used, and in that the control means are designed to control, and if necessary selectively vary, in predetermined ways, as a function of the water hardness indicated by the indicator means, and through said first and second electric valve means (12, 38): * the quantity of water used for forming the brine used for each operation of regenerating the softening substances contained in said first tank, and * the frequency of the operations of regenerating and washing said softening substances. * the quantity of water used for forming the brine used for each operation of regenerating the softening substances contained in said first tank, and * the frequency of the operations of regenerating and washing said softening substances.