A screw spindle pump having a spindle housing in which a drive spindle and at least one running spindle meshing therewith are received in spindle bores, and an external housing which accommodates the spindle housing, an axial inlet connection and a radial outlet connection being provided on the external housing. The spindle housing has an axial fluid outlet for the fluid conveyed via the drive spindle and the running spindle through the spindle housing, as well as a drive motor having a drive shaft which runs through a bore in a housing wall, which axially closes the interior of the external housing, and which is coupled to the drive spindle. A part of the fluid flowing out of the fluid outlet of the spindle housing flows through the seal-free bore along the drive shaft into the drive motor, cools this drive motor and flows back into the external housing.