An apparatus for measuring the mass flow rate of air has a resistance bridge circuit, whose diagonal voltage is applied to a switching control element, which is in turn supplied with voltage pulses for heating a flow sensor probe. The switching control element regulates the heat output conveyed to the probe, and emits an output signal proportional to the mass flow rate of air over the probe. The voltage pulses (U.sub.T) for heating the probe are supplied to a first closed loop control circuit. The first closed loop control circuit emits a first output signal (U.sub.a1), which is a function of the voltage measured across the diagonals of the resistance bridge circuit. A second closed loop control circuit is adapted to receive the first output signal (U.sub.a1) and an input signal (V.sub.2 U.sub.R). The input signal (v.sub.2 U.sub.R) depends on the voltage pulses (U.sub.T) for heating the sensor's probe, a reference variable (U.sub.R), and the first output signal (U.sub.a1). The output of the second closed loop control circuit is the desired analog output signal of the apparatus and is indicative of the mass flow rate of air over the probe.