A pressure actuated single-lumen blood pumping device has a housing (4) having a wall (19) bounding a pressure transfer chamber (11 411). The housing (4) bounds a pressure transfer port (9) for connection to a pressure source, the pressure transfer port (9) communicating with the pressure transfer chamber (11 411) for alternatingly transferring over pressure and under pressure from the pressure source to the pressure transfer chamber (11 411). A flexible tubular membrane (2 102 202 302 402) is arranged in the pressure transfer chamber (11 411). A blood transfer conduit (3 103 203 303 403) passes through the wall (19) bounding the pressure transfer chamber (11 411) and the blood transfer conduit (3 103 203 303 403) connects to opposite ends (5, 6 105 405, 406) of the flexible tubular membrane (2 102 202 302 402).
