A supply group of a packing band from reels, with an automatic change of the reel for an object-packing machine, includes a supply conveyor along which the packing band runs, a device for transversally cutting the band located at a start of the supply conveyor, a device for supporting one reel of the band of slim packing material and a device for supporting a second reel of band of slim packing material. The group includes a first entry conveyor of the first band from the first reel to the supply conveyor, a second entrance conveyor of the second band from the second reel to the supply conveyor, a device for advancing for introducing or extracting the front end of the first band to or from the supply conveyor, and a device for advancing for introducing or extracting a front end of the second band into or from the supply conveyor.