A pump system and a method for pumping viscous or partially viscous media out of a borehole. The pump system includes a well pipe which is installed in the borehole and a motor which is coupled to an eccentric screw pump, the eccentric screw pump including one or more stators and one or more rotors which are received in the stator(s) so as to rotate eccentrically. One or more connection mechanisms fix the eccentric screw pump in the well pipe in a force-fitting and/or formfitting manner. For the purpose of removing the eccentric screw pump from the borehole, the eccentric screw pump is held by means of the one or more connection mechanisms with an axial freedom of movement.