A pumping system comprising a pump (21) for conveying a pumped fluid using an actuating fluid. The pump comprising a rigid outer casing (25) defining an interior space (26), a tube structure (27) accommodated in the interior space (26), the tube structure (27) being flexible and substantially inelastic. The interior of the tube structure (27) defines a pumping chamber (28) for receiving pumped fluid. The tube structure (27) is movable between laterally expanded and collapsed conditions for varying the volume of the pumping chamber (28) thereby to provide discharge and intake strokes. The region of the interior space (26) surrounding the tube structure (27) defines an actuating region for receiving and accommodating actuating fluid. The pumping chamber (28) is adapted to receive pumped fluid to cause the tube structure (27) to move towards the expanded condition and the pumping chamber (28) thereby undergoing an intake stroke. The pumping chamber (28) undergoes a discharge stroke upon collapsing of the tube structure (27) in response to the action of actuating fluid in the actuating region. The pumping system also comprises a delivery means (50) for delivering pumped fluid to the pumping chamber (28) in timed sequence for causing the pumping chamber (28) to undergo an intake stroke, and means (70) for supplying actuating fluid to the actuating region in timed sequence to cause the tube structure (27) to laterally collapse whereby the pumping chamber (28) undergoes a discharge stroke.