The demodulator has an oscillation circuit (1), tuned to the centre frequency of the frequency-modulated input signal (S0), for providing a phase-shifted signal (S2) in dependence on the frequency of the input signal (S1), which is mixed with a signal obtained from the latter. A master-slave frequency divider flip-flop circuit (4) receives the input signal and the inverted input signal at the master flip-flop (4.1) and the slave flip-flop (4.2) respectively, the output of the master flip-flop fed to the oscillation circuit and the output of the slave flip-flop fed to the mixer (2).