A process for the production of tapes from a web of polymeric material, as well as an apparatus for carrying out the process, in which a polymer melt is extruded to form the web, which is then cooled, and drawn off. The web is then cut to form a tape sheet composed of a plurality of tapes. According to the invention, before its drawing, the sheet of tapes is divided into several groups of tapes and drawn separately. For this, a drawing device is provided with which the tapes are drawn separately after division of the sheet of tapes.