An FM demodulator circuit includes a filter (10) and a detector (14) for receiving a frequency modulated input signal and for providing a demodulated output signal. A tuning circuit (19) is provided for tuning the frequency characteristics of the filter and of the detector. A DC offset estimator (18) is connected to the output of the detector to produce an offset signal representing the estimated DC offset of the demodulated output signal, and to provide the offset signal to the tuning circuit. The tuning circuit is operable to tune the frequency characteristics of the filter and detector in dependence upon the offset signal.