Methods and apparatus are described for the production of a crystal slurry during the crystallization step of fractionation processes of edible oils and fats and related oil derivatives. The crystallization process for edible oil and fats is carried out in a crystallizer with stationary heat exchange elements, wherein the contents of said crystallizer are made to move along said heat exchange elements in an oscillatory manner without the use of an internal agitator. The crystallizer for edible oil and fats with stationary heat exchange elements is also described.