A machine for making and dispensing semiliquid and/or semisolid food products includes a working unit equipped with a cylinder for processing a mixture of a basic product and air, a heat exchange fluid flow chamber located around the cylinder, a dispensing tap and a mechanism for treating and feeding the heat exchange fluid to the flow chamber, and a flexible container for containing the basic product. A peristaltic pump transfers the basic product from the container to the processing cylinder through a supply duct along which there is a first pressure sensor for the pressure of the mixture fed into the cylinder. The sensor sends a signal indicating the pressure of the mixture to a control and drive unit which adjusts the operation of the peristaltic pump and thus the output pressure of the pump.
