a process for the manufacture of a multilayer cross - linked , heat - shrinkable , polyolefin film , said film having at least one inner layer comprising thermo - plastic polymer sandwiched between two outer layers comprised of thermoplastic polymer different from the thermoplastic polymer of said inner layer , comprising the steps of a ) coextruding the materials into a tape ; b ) cross - linking it ; c ) converting said cross - linked tape into a heat - shrinkable film by orientation ; characterized in that scrap material produced in the manufacture or in the further processing to finished articles of cross - linked films of this same structure is incorporated by recycling it into said step a ) in an amount up to 50 % by weight of the total film weight .