A pumping device includes a single-use device and a reusable device. The single-use device is to be inserted into the reusable device and includes two pump units in series, one behind the other. Each pump unit includes a rotor for a bearingless motor, and can be magnetically levitated and driven without contact for rotation about an axial direction. The reusable device includes a stator for each rotor which form an electromagnetic rotary drive for rotating the rotor about the axial direction. Each stator is a bearing and drive stator with which the rotor can be magnetically driven and levitated without contact with respect to the stator. An independent control device is provided for each stator, and can independently activate a respective stator.