Abstract: Since the multicomponent signal with nonlinear time-frequency structures occupies a wide frequency band, and the spectral contents of the signal components may alias, it is therefore difficult to separate the signal components and to separate the signal from background noise. In this paper, a new signal separation method using FMmlet transform is proposed taking the advantage that the atoms of FMmlet transform can match both the linear and nonlinear time-varying structures. Theoretical predictions and numerical experiments show the feasibility of the methodology advocated.