A pump includes a suction space, a delivery space and valves. The suction space is at least partly bounded by a flexible body and located between end elements, at least one of which can be driven so as to move in a reciprocating manner. The delivery space surrounds the suction space and around which a housing is provided. The valves are provided in the housing and in at least one of the end elements, and are constructed such that when a volume of the suction space is increased, a medium is sucked into said suction space, and when the volume is reduced, the medium flows through one of the valves to the delivery space, from which it is expelled when the volume of the delivery space is reduced.