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).