Abstract: A rotary displacement pump (2) for pumping a medium, having a pump housing (3); a reception chamber (4) which is formed in the pump housing (3), with an inlet area (26) and an outlet area (27); at least one rotary displacement element (5, 6) which is accommodated in the reception chamber (4), and which is rotatably attached by means of at least one bearing (40, 41, 56) in the pump housing (3), and which presents at least one delimitation surface (21), by means of which it delimits at least one work space (19) of the pump (2); and a bypass (59) which allows the return flow of a part of the pumped medium from the outlet area (27) into the inlet area (26).