This paper reports the results on experimental and theoretical study of the new phenomenon called ion-exchange-isothermal-supersaturation (IXISS). This effect is observed for a number of ion-exchange systems where frontal or reverse frontal separation is accompanied by the formation of extremely stable supersaturated solutions of low solubility substances in the interbed space of ion-exchange columns. After leaving the column a supersaturated solution crystallizes spontaneously, which allows for designing a practically ideal ion-exchange process where a crystalline product is obtained directly after the ion-exchange treatment-cycle. The paper is comprised of results on experimental investigation of IXISS of magnesium carbonate on carboxylic resins which is observed in desorption of Mg2+ from the resin in the Mg form with Na2CO3 solutions or with solutions of Na2CO3-NaHCO3 mixtures. The physical and mathematical models of the ion-exchange processes accompanied by the IXISS effect are proposed and their validity is experimentally confirmed.