Method and circuit for converting, through at least one intermediary frequency, frequency modulated signals into low frequency signals. The intermediary frequency signals are produced by mixing (2) with an oscillator voltage (3) and they are filtered by means of filters (5) and demodulated (6). The resonance frequency of the filter(s) is restituted by means of a control voltage derived from the demodulated signal as a function of the intermediary frequency. To improve the restitution capacity of the filter, the oscillator (3) is so driven as to produce an amplitude drop in the high range of low frequencies. The control voltage intended to the oscillator is also derived from the demodulated low frequency signal while there is provided a phase rotation with an inverter (8) connected in the control circuit of the oscillator.