A process of high-speed spinning of a set of thermoplastic monofilaments having a linear density from 1 to 30 dtex, includes spinning to obtain melt-spun thermoplastic monofilaments and airblast cooling of the melt-spun monofilaments. To produce a particularly fine monofilament at high winding speeds, the process also includes guiding the thermoplastic monofilaments directly over a fork-like friction element having axially parallel, spaced apart upper and lower contacting friction surfaces during the airblast cooling, and then spin finishing and winding up the thermoplastic monofilaments. An apparatus for melt-spinning including the friction element is described. The product monofilament produced by the process can have an elongation of 20 to 45%, a strength of 36 to 60 cN/tex; a boil shrinkage of 2 to 15%; an Uster % less than 1 and a uniformly round cross section.