A system for the processing and separation of biological fluids into components, the system comprising an apparatus that cooperates with a disposable set, the apparatus comprising a cabinet for housing a hollow centrifugal processing chamber of the disposable set, the disposable set comprising: (a) a set of flexible containers (40,42-44) for receiving biological fluid to be separated and separated components, and optionally one or more additional flexible containers for additive solutions, (b) the set of flexible containers being interconnected by tubing associated with valves for controlling the input and the extraction of fluids into or from the containers, and (c) a hollow centrifugal processing chamber rotatable about an axis of rotation and having an axial inlet/outlet for the biological fluid to be processed and for the processed components of the fluid, the processing chamber containing an axially movable member which defines a separation space of variable size for receiving biological fluid, the member being axially movable to intake a selected quantity of biological fluid to be processed into the separation space via said inlet and to express processed biological fluid components from the separation space via said outlet, the hollow centrifugal processing chamber of the disposable set being receivable in the apparatus' cabinet, each of said centrifugal processing chambers being rotatable about a central axis of rotation of the centrifugal processing chamber, the cabinet comprising drive means for rotatably driving a hollow centrifugal processing chamber received therein about the central axis of rotation of the centrifugal processing chamber, and means for monitoring the position of the axially movable member to control the amounts of intaken and extracted fluids, characterised in that the apparatus' cabinet comprises a plurality of side-by-side locations for receiving in the cabinet a corresponding plurality of centrifugal processing chambers in side-by-side spaced-apart relation, each of said side-by-side locations comprising an individual drive means for driving its centrifugal processing chamber about its centraé axis of rotation; the valves associated with the disposable sets are remotely-actuable valves located on the apparatus' cabinet in the proximity of the locations for receiving the respective centrifugal processing chambers; and the apparatus further comprises means for actuating the remotely actuable valves individually and by combinations of individual actuations, these valve-actuating means including a control panel that provides a display of the state of actuation whether open or closed of individual remotely-actuable valves, the selection of the state of actuation of the individual actuable valves being arranged to control connection of the centrifugal processing chamber of each fitted disposable set with the flexible container of the same disposable set or to another container, and to contol connection of the centrifugal processing chambers with the flexible containers or other containers of several fitted disposable sets in different combinations, in particular with series and/or parallel connections. (a) a set of flexible containers (40,42-44) for receiving biological fluid to be separated and separated components, and optionally one or more additional flexible containers for additive solutions, (b) the set of flexible containers being interconnected by tubing associated with valves for controlling the input and the extraction of fluids into or from the containers, and (c) a hollow centrifugal processing chamber rotatable about an axis of rotation and having an axial inlet/outlet for the biological fluid to be processed and for the processed components of the fluid, the processing chamber containing an axially movable member which defines a separation space of variable size for receiving biological fluid, the member being axially movable to intake a selected quantity of biological fluid to be processed into the separation space via said inlet and to express processed biological fluid components from the separation space via said outlet,