Packaging machine for producing bag packages, and bag package

A horizontal bag-making machine having a packaging material delivery unit, a product delivery unit, and a folding, sealing, and separating unit for folding the packaging material into a tube, sealing the folded packaging material in the directions transverse and parallel to a conveying direction and for cutting the packaging material into individual bag packages also has a tear-open assistance unit located in the conveying direction between the product delivery unit and the folding, sealing, and separating unit. The tear-open assistance unit produces an overlap of material in the separation region, the overlap of material extending at least approximately transversely to the conveying direction of the packaging material, and releasably fixes the overlap of material in the separation region. The bag packages produced in this way are easy to open yet are still in accordance with stringent hygiene regulations.