(57) A rotary pump having an eccentric rotor (14) adapted to effect eccentric motion relative to the axis of the pump shaft (7) within a pump casing (1) to cause pumping action in a pump chamber. The pump comprises a pump casing (1), a pump shaft (7) mounted on the pump casing, a pair of eccentric rotors (14) mounted on the pump shaft (7) with angular spacing apart of 180°, a pair of diaphragms (24) on the eccentric rotors (14) to define a pair of pump chambers P, a partition member (36) adapted to divide the pump chamber into a suction chamber (Pi) and an exhaust chamber (Pe), and an intake port (42) and an exhaust port (43) in communication with the suction and exhaust chambers, respectively, the intake port being cut off from its communication with the exhaust port by the partition member during rotation of the pump shaft.