In a process for the biaxial stretching of a flat film web from plastics material in a stretching apparatus in which the edges of the flat film web are retained by grippers driven by means of threaded spindles, and at least part of the stretching in longitudinal direction is being effects by means of a progressive pitch of threaded spindles simultaneously with at least part of the transverse stretching, the modification wherein the film is stretched in longitudinal direction at up to 10% in excess of the stretching degree desired in the finished film and, subsequently to the stretching in longitudinal direction, is shrunk to the desired stretching degree in longitudinal direction, while the film web is still being further stretched in transverse direction, by guiding the grippers in a degressive thread pitch.