Abstract: The invention relates to a fluid-conveying machine, in particular, a pump having a component rotating in a stationary housing part inside an annular gap. The stationary housing part separates an interior having a higher product pressure from an exterior having a lower pressure. A rotating component is mounted in an external bearing which is sealed with respect to the interior via a sealing system. In order to improve the sealing, the invention provides that the annular gap is formed between two sliding bearing shells which comprise extremely hard, wear-resistant materials and, in accordance with the operating principle of a radial sliding bearing, form a first pressure-reducing stage. A feedback device, which feeds back the leakage from this first sealing stage into the conveying process of the machine, is connected downstream of the first pressure-reducing stage. A second sealing stage is arranged axially downstream of the feedback device.