Abstract: The invention relates to a process and an apparatus for forming molten drops of precursors of thermoplastic polyesters or copolyesters as molten monomer, oligomer, monomer/glycol mixture or after partial polycondensator [sic] and melting to give a molten precursor, in which the precursor formed into drops is introduced into a gaseous medium, and the gaseous medium, after entry of the precursor formed into drops into the gaseous medium, accelerates the crystallization process by holding the drop-form precursor at a temperature above 100° C. and below its melting point for a limited time until crystallization of the drop at the surface of the precursor is complete. To this end, the apparatus has a fall tower, through which the gaseous medium flows in countercurrent from bottom to top, while the drops fall in the vertical direction from top to bottom into a collecting funnel with a precrystallized surface.