The machine has a compression surface and a conveying surface (FF) over which packets of nappies are transported from a nappy supply point to a bagging point. The packets move over the surfaces by an air cushion created by a system of air jets (LD). The surfaces may lie along two, and preferably three or four, sides of the packets. They may be formed from metal plates (2) and profiles which have one or more nozzle hole sections (A) and at least one air blowing connection (6).