A system and process for packaging groups of products, such as spirally wound paper products are disclosed. During the packaging of groups, a continuous supply of a wrapping material is unwound and cut periodically in the edge regions. Optionally, a perforation line may also be formed into the wrapping material in between the two cut edges. The cut edges form flaps that are then wrapped around the product groups and sealed. The wrapping material is then broken along the perforation lines in order to form individual packages. Finally, the ends of the packages are folded and sealed.