A method and an apparatus for producing a highly oriented yarn (HOY) wherein the yarn is withdrawn from the nozzle of a spinneret at a withdrawal speed of at least 6,500 m/min. The filaments forming the yarn are drawn during their solidification, so that a highly oriented molecular structure forms in the polymer. To withstand the withdrawal tension generated by the high withdrawal speed without overstressing the filaments, the filaments are assisted in their advance before they solidify such that prior to the solidification a tensile stress relief is effective on the filaments, and that during the solidification a reduced withdrawal tension is effective on the filaments while they are drawn.