Abstract: The invention includes an operating method for the continuous purification of a liquid utilizing either single or dual ion exchange vessels, each vessel being physically divided into one or more discrete of ion exchange zones, each zone having an inlet and an outlet. A valving means at the inlet and outlet of each ion exchange zone provides communication between adjacent ion exchange zones as well as to feed, product, water and regenerant chemical streams. In one aspect of this invention a first vessel contains a discrete plurality of cation exchange zones and a second vessel contains a discrete plurality of anion exchange zones. In another aspect of this invention, a single vessel contains a plurality of discrete cation exchange zones and a plurality of discrete anion exchange zones. In another aspect of the invention, each ion exchange zone is contained within a single vessel.