A method of melt spinning a group of multifilament yarns (1) from a polymer melt, wherein each group of yarns (10) is formed from a plurality of filaments (4) that are extruded through a nozzle bore (3) and withdrawn by a withdrawal means by the action of a withdrawal tension. In accordance with the invention, each group of yarns (10) is cooled in a precooling zone (5) and in an aftercooling zone (6) downstream thereof. The cooling in the precooling zone (5) and in the aftercooling zone (6) is adjusted such that the group of yarns (10) is cooled within the aftercooling zone (6) by the action of a coolant flow directed into the path of the yarn, so that the filaments (4) of the group of yarns (10) solidify in a solidification range within the aftercooling zone (6).