Described is a machine (1) for making liquid or semi-liquid food products comprising: a frame (2); a plurality of first containers (3) containing a liquid or semi-liquid basic mixture and having a deformable wall (4), in such a way that the space occupied by each first container (3) depends on a quantity of basic mixture in the first container (3); a rigid second container (5) forming a processing chamber for the basic mixture and equipped with a mixer (6) and means (7) for thermal treatment of the basic mixture, operating in conjunction with one another to convert the basic mixture into a liquid or semi-liquid product; means (8) for connecting the first containers (3) to the second container (5), configured to allow connection of one of the first containers (3) to the second container (5) and for transferring the basic mixture from one of the first containers (3) to the second container (5); means (9) for supporting the first containers (3), operatively associated with the frame (2), at least one sensor (10) configured for making available a signal representing the quantity of basic mixture at least in one of the first containers (3) operatively connected to the second container (5); a command and control unit (11), connected to the sensor (10) to receive the signal and configured to infer, based on the signal, a condition of absence of mixture in one of the first containers (3) connected to the second container (5).