Electromechanical amplifying method comprising at least: - a first transducing step consisting in transducing an electrical signal to a microsystem or nanosystem mechanical resonator having a mechanical resonance mode of angular frequency ω 0, said electrical signal actuating nonlinear oscillations of the resonator according to a non-linear differential Duffing equation with a non-zero Duffing coefficient; - a second transducing step consisting in transducing the non-linear oscillations of the resonator into a transduced electrical signal; and - a filtering step consisting in filtering said transduced electrical signal to obtain an output signal; wherein - the signal transduced to the resonator during the first transducing step is obtained by adding a first input signal of a first amplitude and of a first angular frequency ω s and a second pump signal of a second amplitude greater than the first amplitude and of a second angular frequency ω ρ that is different from the first angular frequency, the first and second angular frequencies being close to the angular frequency ω 0 of the mechanical resonator and the second pump signal being chosen from a range of angular frequencies ω ρ and amplitudes in which the resonator is actuated in a non-linear regime; and - the output signal is amplified, the method being characterised in that: the amplitude of the oscillations measured after the filtering varying linearly with the first input signal of the angular frequency ω s and the resonant mode obtained is that of a linear resonance, and in that the difference δ s between the first and second angular frequencies, defined by "ω s - ω ρ " is at least fifty times smaller than the angular frequency ω 0 of the resonator and the difference δ ρ between the second angular frequency and the angular frequency ω 0 of the resonator, defined by "ω ρ - ω 0 ", is at least fifty times smaller than the angular frequency ω 0 of the resonator; and in that the filtering step is performed with a bandpass filter of which the bandwidth is centred on the angular frequency ω 0 of the mechanical resonator or on an angular frequency equal to ω ρ + δ s. the amplitude of the oscillations after filtering being measured at the angular frequency "ω ρ + δ s ". - a first transducing step consisting in transducing an electrical signal to a microsystem or nanosystem mechanical resonator having a mechanical resonance mode of angular frequency ω 0, said electrical signal actuating nonlinear oscillations of the resonator according to a non-linear differential Duffing equation with a non-zero Duffing coefficient; - a second transducing step consisting in transducing the non-linear oscillations of the resonator into a transduced electrical signal; and - a filtering step consisting in filtering said transduced electrical signal to obtain an output signal; - the signal transduced to the resonator during the first transducing step is obtained by adding a first input signal of a first amplitude and of a first angular frequency ω s and a second pump signal of a second amplitude greater than the first amplitude and of a second angular frequency ω ρ that is different from the first angular frequency, the first and second angular frequencies being close to the angular frequency ω 0 of the mechanical resonator and the second pump signal being chosen from a range of angular frequencies ω ρ and amplitudes in which the resonator is actuated in a non-linear regime; and - the output signal is amplified, the amplitude of the oscillations measured after the filtering varying linearly with the first input signal of the angular frequency ω s and the resonant mode obtained is that of a linear resonance, and in that the difference δ s between the first and second angular frequencies, defined by "ω s - ω ρ " is at least fifty times smaller than the angular frequency ω 0 of the resonator and the difference δ ρ between the second angular frequency and the angular frequency ω 0 of the resonator, defined by "ω ρ - ω 0 ", is at least fifty times smaller than the angular frequency ω 0 of the resonator; and in that the filtering step is performed with a bandpass filter of which the bandwidth is centred on the angular frequency ω 0 of the mechanical resonator or on an angular frequency equal to ω ρ + δ s. the amplitude of the oscillations after filtering being measured at the angular frequency "ω ρ + δ s ".