Method and appliance for carrying out membrane electrophoresis using microfiltration or ultrafiltration membranes, wherein the electroosmotic flow which develops in the membrane pores is reduced or offset by pressure superposition. The appliance for the membrane electrophoresis comprises at least an at least quadrupartite separation chamber (7), having at least one diluate space (16) and one concentrate space (17) and also a cathode space (18) and an anode space (21) having electrodes as anode (19) and cathode (20), with the individual spaces (16, 17, 18, 21) being separated from each other by ultrafiltration or microfiltration membranes (14, 15); feed lines (22) and discharge lines (23) for the diluate, feed lines (24) and discharge lines (25) for the concentrate, optionally feed lines (26) and discharge lines (27) for the electrode rinsing solution, and also a device (8; 10) or (9; 11) for pressure regulation by means of which a pressure difference, in particular of at least 3 kPa, can be generated between the diluate space (16) and the concentrate space (17).