Nonlinearities characterization and identification of acoustical systems is an active research field, notably in the area of electroacoustics. An innovative characterization and identification method, based on the nonlinear convolution and the use of a synchronized swept-sine excitation signal, has recently been developped. In this paper, this method is applied to the study of the nonlinearities exhibited by the mechanical suspensions of an electrodynamic loudspeaker. Nonlinear behaviours are specially studied as function of the amplitude of the displacement of the membrane of the loudspeaker. In this context, we develop an experimental setup from the signal generator to the mobile part of the tested component, specially designed in order to obtain a great harmonic distortion measurement dynamic range and, thus, to allow the measurement of weak nonlinearities. Nonlinearities are estimated for both the external and internal suspensions independently, and for several kinds of loudspeakers. Results are compared with those obtained by other methods available in the literature.