An intravascular blood pump having a drive section (11), a catheter (14) fastened to the drive section proximally and a pump section (12) fastened to the drive section distally possesses an electric motor (21) whose motor shaft (25) is mounted in the drive section (11) with two radial sliding bearings (27, 31) and an axial sliding bearing (40). During operation, purge fluid is conveyed through the bearing gap of the axial sliding bearing (40) and further through the radial sliding bearing (31) at the distal end of the drive section (11). The purge fluid is highly viscous, for example 20% glucose solution.