A machine (1) for making liquid or semi-liquid food products comprises: a plurality of supply containers (3) containing a liquid or semi-liquid basic mixture and comprising a deformable wall (4), so that the space occupied by each first container (3) depends on a quantity of basic mixture in the self-same first container (3)； a processing container (5) forming a processing chamber for the basic mixture and provided with a stirrer (6) and with thermal treatment means (7) for the basic mixture, operating in conjunction with one another to convert the basic mixture into a liquid or semi-liquid product； connecting means (8) for connecting the supply containers (3) to the processing container (5), configured to allow the operative connection of one of the supply containers (3) to the processing container (5) and to transfer the basic mixture from one of the supply containers (3) to the processing container (5)； an electronic drive and control unit (11), the connecting means (8) comprising a plurality of pneumatically operated closing valves (19), where each of the valves is associated with one of the supply containers (3) and can be activated and deactivated independently of the remaining valves (19) to allow the placement of one of the containers (3) in connection with the processing container (5).
