The invention relates to a double-row rolling-element bearing unit (9) of a medical pump (1), preferably syringe pump, which rolling-element has a bearing core (19), which forms a first inner running surface (26) for first rolling elements (24), which first inner running surface faces in an axial direction, and forms a second inner running surface (27) for second rolling elements (28), which second inner running surface is arranged oppositely to the first inner running surface (26) in the axial direction. Furthermore, the pump (1) has a bearing bush (14), which can be mounted on a housing portion (10) and forms a first outer running surface (23), which lies opposite the first inner running surface (26), and the pump has a bearing cup (17), which forms a second outer running surface (29), which lies opposite the second inner running surface (27). At least one preloading element (16) is provided, which couples the bearing cup (17) to the bearing bush (14) with a defined preload in order to join the double-row rolling-element bearing unit (9) as a unit.