In a countercurrent, cooling crystallization and purification method for a multi-component molten mixture for separating a component of the mixture, wherein the purification of the molten mixture is effected by countercurrent contact of crystals formed with a mother liquor, wherein the improvement comprises, in a system comprising a plurality of cooling type crystallizers each having, at their respective upper portions, a clarifying portion containing a liquid, and a vertical purifier having, at its upper portion, a clarifying portion and, at its lower portion, heating means, feeding said molten mixture into one of said crystallizers, effecting crystallization in each of the crystallizers at different temperatures, said purifier being operated at a temperature higher than any of the crystallizers, feeding a slurry containing crystals formed in each of the crystallizers to the clarifying portion of another of the crystallizers wherein the crystallization is effected at a higher temperature and feeding a slurry containing crystals formed in the crystallizer wherein the crystallization is effected at the highest temperature among the crystallizers to the clarifying portion of the purifier, allowing the crystals in the purifier to move downwardly therein and melting said crystals by said heating means, withdrawing a portion of the resulting melt as a product and allowing the remainder of said melt to move upwardly as a reflux in said purifier to wash the descending crystals, feeding the clarified liquids from the clarifying portions of the purifier and the crystallizers directly to the liquids in the respective clarifying portions of the crystallizers of sequentially lower temperature so that crystals formed in each of the crystallizers of sequentially lower temperature are washed and the clarified liquid fed into each crystallizer from the crystallizer of sequentially higher temperature or from the purifier, respectively, is cooled by the liquid of lower temperature in the crystallizer of sequentially lower temperature to be recrystallized, and discharging the clarified liquid in the crystallizer of the lowest temperature from the system.