A bearing unit for a turbocharger, including a bearing housing extending in an axial direction and also including a bearing cartridge arranged within the bearing housing, wherein between the outer circumference of the bearing cartridge and the bearing housing there is formed an intermediate space with an oil film, and wherein the bearing housing has a supply bore formed for the supply of oil to the oil film. The bearing cartridge includes a rolling bearing, the outer cartridge ring of which is mounted in a freely rotatable manner in the oil film. A bearing unit for a turbocharger, the bearing cartridge of which includes a rolling bearing, the bearing outer ring of which is mounted in a freely rotatable manner in the oil film. By means of bearing units of such design, it is possible to ensure the secure mounting of a shaft even without a separate twist prevention device.