The system comprises: a first tank (24) for water-softening substances, with at least an inlet opening (26) for water to be softened and an outlet opening (28) for softened water, - a second tank (30) for salt, with a water inlet opening (32) and an outlet opening (34) for a regenerating brine formed following the dissolution of the salt in the water, a line (36) connecting the second tank (30) to the first tank (24) for the outflow of the brine towards the first tank (24), a water supply line (10) having a branch-off point (18) into a first branch (20) supplying the first tank (24) and into a second branch (22) which leads to the inlet opening (32) of the second tank (30), a first electric valve (12) for controlling the flow of water through said supply line (10), a second electric valve (38) for controlling a flow of water towards and through the second tank (30) for forming the brine, devices (14) for determining the amounts of water used for washing the dishes, forming the regenerating brine and washing the softening substances after a regenerating operation; an indicator (50) adapted to supply signals or data indicative of the hardness of the water used, and - an electronic control unit (ECU) designed to control predetermined parameters of the regeneration of the water-softening substances and if necessary to vary these parameters selectively in predetermined ways, as a function of the hardness of the water, and through the electric valves (12, 38).