The invention is an ink supply system (2) for an inkjet printer (1) with a print head assembly (6) comprising at least one print head (7) with one or more nozzles (8) for at least one colour, in which the print head (7) is linked via a first connection line (19) with a supply tank (17), which is connected with an intermediate tank (12) via a filler line with interconnected conveyance means (16) and filter assembly (18), and also via a second connection line (21) with a return tank (22) and with the means (32) to generate a vacuum, through which the pressure differential in the supply tank (17) and/or return tank (22) can be controlled if necessary, which controls a flow of the ink from the supply tank (17) via at least one flow channel (20) in the print head (7) to the return tank (22) and the return tank (22) is linked with the intermediate tank (12) via a return line (24), where applicable also with interconnected conveyance means (25), whereby a closed ink circuit (for standard printing operations) is maintained, whilst also facilitating the reversal of the ink flow through the respective switching of the vacuum system (35) to the supply tank and subsequent emptying of the ink backflow via the drainage line (26) back into the intermediate tank (12), resulting in increased operating reliability of the print heads due to the washing out of any deposits from the flow channels (20).