A device for supplying and/or aspirating a fluid substance to or from a human or animal body is provided, which device has a drive unit with a drive, an attachment part which is attachable to the drive unit, and also a coupling element. The attachment part has a peristaltic pump unit with a pump head having one or more roller elements which are movable freely and independently of one another and serve for rolling on a hose. The coupling element serves to transmit a movement from the drive to the pump head. The pump head has a state in which it is decoupled from the coupling element, and in which the one or more roller elements apply no mechanical pressure or a comparatively low mechanical pressure to the hose, and also a state in which it is coupled to the coupling element, and in which the one or more roller elements are pressed by the coupling element against the hose with a comparatively high mechanical pressure.
