Process for forming drops of precursors of thermoplastic polyesters or copolyesters as molten monomer, oligomer, monomer/glycol mixture or after partial polycondensation and melting to give a molten precursor, in which the precursor formed into drops is introduced into a gaseous medium, characterized in that the gaseous medium, after entry of the precursor formed into drops into the gaseous medium, accelerates the crystallization process of the precursor and brings about the crystallization state of the precursor in an accelerated manner 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.