A pump system for conveying a first fluid using a second fluid. The system includes at least a first pump having at least a first rigid outer casing defining a first interior space and a first flexible tube structure accommodated in the first interior space. The interior of the first flexible tube structure is arranged for receiving one of the first or second fluids. The region of the first interior space surrounding the first flexible tube structure is arranged for receiving the other of the first and second fluids. The first flexible tube structure is movable between laterally expanded and collapsed conditions for varying the volume of the interior of the first flexible tube structure, thereby imparting sequential discharge and intake strokes on the first fluid.