A system (1) for release or movement of a fluid-dispensing head (2) positioned within a dispenser (6) of fluids; the system (1) houses the fluid-dispensing head (2), which has a plurality of nozzles (3) for the supply of fluids; the system (1) comprises means (7, 10, 20) for release and movement of the fluid-dispensing head (2) configured for enabling movement of the delivery head (2) between a first position of use, in which the nozzles (3) deliver the plurality of fluids into a container (4), and a cleaning position or second position of use (set facing the operator) or third position of use (facing upwards), distinct from the first position of use, in which they are accessible for being cleaned.