A pump comprising, a first fluid port and a second fluid port, a housing having an interior surface defining a cavity, and a rotor located in the cavity, the rotor being rotatably mounted within the housing and having a longitudinal axis of rotation, the rotor comprising a housing engaging surface area forming a sealing interference fit with the interior surface of the housing, and a surface recess that forms with said interior surface of the housing a fluid-conveying chamber that, on rotation of the rotor, conveys fluid from the first fluid port to the second fluid port, characterized by a plurality of resiliently deformable diaphragms each providing part of the interior surface of the housing, each diaphragm comprising a rotor engaging surface and a rear surface opposite the rotor engaging surface, the rotor engaging surface of each diaphragm being urged into contact with the rotor by the action of a pressurising means acting on the rear surface of the diaphragm, the number of resiliently deformable diaphragms exceeding the number of surface recesses on the rotor, the rotor comprising an elongate body and a drive shaft, which body is substantially hollow and comprises separate first and second rotor cavities, the first rotor cavity having an opening at a first end of the rotor and the second rotor cavity having an opening at a second end of the rotor, the rotor body further comprising a first opening between the first rotor cavity and the surface recess and a second opening between the surface recess and the second rotor cavity, the pump being arranged such that, when the rotor body is located within the housing cavity, the first fluid port is in fluid flow communication with the first rotor cavity via the opening at the first end of the rotor, and the second fluid port is in fluid flow communication with the second rotor cavity via the opening at the second end of the rotor, and the pump being arranged such that at least one of the resiliently deformable diaphragms always bisects the first opening and the second opening on the rotor surface recess as the rotor rotates. a first fluid port and a second fluid port, a housing having an interior surface defining a cavity, and a rotor located in the cavity, the rotor being rotatably mounted within the housing and having a longitudinal axis of rotation, the rotor comprising a housing engaging surface area forming a sealing interference fit with the interior surface of the housing, and a surface recess that forms with said interior surface of the housing a fluid-conveying chamber that, on rotation of the rotor, conveys fluid from the first fluid port to the second fluid port, characterized by a plurality of resiliently deformable diaphragms each providing part of the interior surface of the housing, each diaphragm comprising a rotor engaging surface and a rear surface opposite the rotor engaging surface, the rotor engaging surface of each diaphragm being urged into contact with the rotor by the action of a pressurising means acting on the rear surface of the diaphragm, the number of resiliently deformable diaphragms exceeding the number of surface recesses on the rotor, the rotor comprising an elongate body and a drive shaft, which body is substantially hollow and comprises separate first and second rotor cavities, the first rotor cavity having an opening at a first end of the rotor and the second rotor cavity having an opening at a second end of the rotor, the rotor body further comprising a first opening between the first rotor cavity and the surface recess and a second opening between the surface recess and the second rotor cavity, the pump being arranged such that, when the rotor body is located within the housing cavity, the first fluid port is in fluid flow communication with the first rotor cavity via the opening at the first end of the rotor, and the second fluid port is in fluid flow communication with the second rotor cavity via the opening at the second end of the rotor, and the pump being arranged such that at least one of the resiliently deformable diaphragms always bisects the first opening and the second opening on the rotor surface recess as the rotor rotates.