In a peripheral pump, having a rotor (2) which rotates in a pump casing (1) and having two delivery chambers (11, 12), which extend on both sides of the end sides (3, 4) and each have circular cross sections, the delivery chambers (11, 12) have a communicating passage (13) between them, formed by an overlap of their cross sections. As a result, the liquid can flow without interference from one delivery chamber (11) into the other delivery chamber (12). One delivery chamber (11) is connected to an inlet duct, while the other delivery chamber (12) is connected to an outlet duct.