Time–frequency analysis has become a powerful tool for processing nonstationary signals and is widely used in mechanical condition monitoring and system parameter identification under nonstationary operating conditions. However, conventional time–frequency methods have difficulty effectively handling nonlinear multicomponent signals with closely spaced frequency components or even crossing frequency trajectories. This work is devoted to develop an Adaptive Quadratic Chirplet Transform (AQCT) method. The approach computes the Quadratic Chirplet Transform (QCT) of the signal, in which a quadratic frequency modulation parameter is explicitly incorporated. The maximum amplitude signal is then iteratively extracted from the residual QCT, and the QCT contribution of the detected component is removed from the residual representation. Finally, an accurate time–frequency representation of the signal is constructed based on all detected components. Simulation examples and a three-degree-of-freedom spring–damper system model demonstrate that the proposed AQCT method can clearly extract the time–frequency representations of signals with closely spaced frequency components and crossing frequency trajectories, and that it effectively overcomes the limitations of conventional time–frequency transforms in dealing with higher-order frequency variations.