A control system controlling the line pressure in a blood supply system (1) in which a pump (14) pumps blood from a reservoir (10) via a primary passage (18) toward a plurality of outlets (16, 26, 26a), wherein one or more outlets are openable to permit flow and closable to block flow, said control system comprises a monitoring arrangement to determine a line pressure in the primary passage, and a controller responsive to the monitoring arrangement and controlling the pump (14) to maintain the line pressure in the primary passage (18) above a pre-set level. The control system practically eliminates the risk of a momentary reduction in blood supply line pressure when an outlet is opened.