A machine for making and dispensing semiliquid and/or semisolid food products comprising a working unit (3) equipped with a cylinder (4) for processing a mixture of a basic product and air, a heat exchange fluid flow chamber (5) located around the cylinder (4), a dispensing tap (6) and means (7) for treating and feeding the heat exchange fluid to the flow chamber (5), is equipped with a flexible container (8) for containing the basic product a peristaltic pump (13) transfers the basic product from the container (8) to the processing cylinder (4) through a supply duct (10) along which there is a first pressure sensor (35) for the pressure of the mixture fed into the cylinder (4) the sensor (35) sends a signal indicating the pressure of the mixture to a control and drive unit (25) which adjusts the operation of the peristaltic pump (13) and thus the output pressure of the pump.