Abstract: This invention relates generally to systems for handling biological fluids such as blood and more particularly relates to apparatus for maintaining a constant flow rate of fluid by a peristaltic pump when the pressure at the input of such a pump goes negative or positive. More specifically, the invention uses a microprocessor which provides an output signal representative of the incremental change in pump speed required when the pump input experiences a negative or positive pressure regime.The microprocessor output is based on a sensed input pump pressure, P.sub.o, a pressure, P.sub.i, which is the pressure at which extensions of the linearly decreasing portions of the pump characteristic curves intersect the pressure axis on a plot of Pressure vs Flow Rate for a given pump and a desired flow rate, Q.sub.o. The resulting output is applied to a stepper motor via a programmable timer and driver amplifier.