A tubular bag-making machine for forming a flexible tube from a hot-sealable web of packaging material sealed longitudinally by means of a longitudinal seam sealing device and transversely by means of a transverse seam sealing device to produce individual tubular bag packages. To improve the transverse sealing seams, bores which can be made to communicate in alternation with a negative-pressure source or an overpressure source are embodied in the sealing jaws of the transverse seam sealing device in regions having a reduced number of layers of packaging material to enable a good heat transfer and a higher sealing pressure in the region of changes in the number of layers of packaging material of the transverse sealing seams.
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