The package of bags consists of two bag stacks 11 and 12 which overlap each other. Each bag 13 of one stack 11 is joined to a bag 14 of the other stack 12 at its upper end in an interrupted portion 19 forming a perforation 15. The overlapping interrupted portions 19 are connected to each other by a heat penetration weld 21 which extends through all the interrupted portions 19. The method consists in the fact that, in a stack 11, 12 of tubular portions which are closed on all sides, two separation incisions are made which separate this stack into two bag stacks 11 and 12 in such a way that in each case two bags 13 and 14 of these two stacks 11 and 12 are joined together by the interrupted portion 19 which separates the separation incisions from one another, that then these interrupted portions 19 are connected to one another by a heat penetration weld 21 and the two bag stacks 11 and 12 are folded onto each other. The apparatus has a base for the stack 11, 12 of the closed tubular portions and a tool, by means of which the separation incisions and the heat penetration weld 21 can be made at the same time. IMAGE
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