A pump comprising: a first fluid port; a second fluid port; a housing having an interior surface defining a cavity; a rotor (30; 230) located in the cavity, the rotor being rotatably mounted within the housing and having a longitudinal axis of rotation, and comprising, a housing engaging surface area forming a sealing interference fit with the interior surface of the housing, and at least one surface recess (231a-231d) that forms with said interior surface of the housing a fluid-conveying chamber (232a-232d) that, on rotation of the rotor, conveys fluid from the first fluid port to the second fluid port; and a resiliently deformable diaphragm (50; 226) providing part of the interior surface of the housing, the diaphragm comprising a rotor engaging surface and a rear surface opposite the rotor engaging surface, the rotor engaging surface of the diaphragm being urged into contact with the rotor by the action of a pressurising means acting on the rear surface of the diaphragm; characterized in that the pump further comprises a pair of flow channels (41a, 41b; 241a, 241b) being associated with the resiliently deformable diaphragm, the flow channels extending longitudinally from opposite ends of the rotor to overlie the surface recess of the rotor, as the rotor rotates in use, the pair of flow channels comprising a first flow channel in fluid communication with the first fluid port and being closed to the second fluid port and a second flow channel being closed to the first fluid port and being in fluid communication with the second fluid port, with each flow channel being located at opposite sides of the diaphragm. a first fluid port; a second fluid port; a housing having an interior surface defining a cavity; a rotor (30; 230) located in the cavity, the rotor being rotatably mounted within the housing and having a longitudinal axis of rotation, and comprising, a housing engaging surface area forming a sealing interference fit with the interior surface of the housing, and at least one surface recess (231a-231d) that forms with said interior surface of the housing a fluid-conveying chamber (232a-232d) that, on rotation of the rotor, conveys fluid from the first fluid port to the second fluid port; and a resiliently deformable diaphragm (50; 226) providing part of the interior surface of the housing, the diaphragm comprising a rotor engaging surface and a rear surface opposite the rotor engaging surface, the rotor engaging surface of the diaphragm being urged into contact with the rotor by the action of a pressurising means acting on the rear surface of the diaphragm; characterized in that the pump further comprises a pair of flow channels (41a, 41b; 241a, 241b) being associated with the resiliently deformable diaphragm, the flow channels extending longitudinally from opposite ends of the rotor to overlie the surface recess of the rotor, as the rotor rotates in use, the pair of flow channels comprising a first flow channel in fluid communication with the first fluid port and being closed to the second fluid port and a second flow channel being closed to the first fluid port and being in fluid communication with the second fluid port, with each flow channel being located at opposite sides of the diaphragm.