The apparatus for cooling, stabilizing and preparing melt-spun filaments includes a spinneret assembly for producing an annular bundle of filaments; a blowing air dispensing device downstream of the spinneret assembly and centrally located in the annular bundle for cooling the melt-spun filaments; a hollow, air-conducting preparation application device located centrally in the annular bundle and downstream of the blowing air dispensing device; a radially closed hollow cylindrical tube having open ends and connecting the blowing air dispensing device and the preparation application device to conduct air flowing through the preparation application device to the blowing air dispensing device and having a length of from 200 to 2000 mm and a controlling device for regulating the spinning speed and filament denier so that the product of the spinning speed and the square root of the filament denier is between 5000 and 20000 (m/min dtex.sup.1/2) to produce cooled prepared filaments with a birefringence not varying from a mean value by more than about 10%.