A dialyser has a membrane assembly (12) comprising two superposed conduits partially define, and separated, by a transfer membrane wall. The walls of the conduit are provided with furrowing (38 or 39) extending with a component along the conduits. Blood is pumped through one conduit by a roller pump (21) and dialysate is pumped in counter current through the other conduit by a roller pump (24), The conduits communicate with separate chambers in flexible bladders (16) along each side edge of the conduits and the bladders are alternately compressed by rollers (27) to provide a superimposed reciprocatory flow component on the blood and dialysate in a direction transverse to the length of the conduits. This reciprocatory flow component, in conjunction with the furrows, produces vortexes in, and good mixing of, the blood and dialysate in their respective conduits and hence enhanced contact of each of these liquids with the transfer membrane wall.