A machine for making liquid or semi-liquid food products includes a plurality of supply containers containing a basic mixture and deformable wall, so the space occupied by each first container depends on a quantity of basic mixture therein. A processing container includes a stirrer and thermal treatment system, operating with one another to convert the basic mixture into a liquid or semi-liquid product. A connecting system connects the supply containers to the processing container to transfer the basic mixture from one of the supply containers to the processing container and includes a plurality of pneumatically operated closing valves, where each of the valves is associated with one of the supply containers and can be activated and deactivated independently of the remaining valves to allow the placement of one of the containers in connection with the processing container.
