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Trajectory piecewise-linearization-based reduced- order macromodeling methods have been proposed to characterize the time-domain behaviors of large strongly nonlinear systems. However, all these methods rely on frequency-domain model-order-reduction (MOR) methods for linear systems. Therefore, the accuracy of the reduced-order models in time domain cannot always be guaranteed and controlled. In this paper, a wavelet-collocation-based trajectory piecewise-linear approach is proposed for time-domain MOR of strongly nonlinear circuits. The proposed MOR method is performed in time domain and is based on a wavelet-collocation method. Compared with nonlinear MOR methods in frequency domain, the proposed method in time domain maintains higher accuracy for modeling transient characteristics of nonlinear circuits, which are very important in macromodeling and transient analysis for nonlinear circuits. Furthermore, a nonlinear wavelet companding technique is developed to control the modeling error in time domain, which is useful for balancing the overall modeling error over the whole time region and improving the simulation efficiency at higher level. The numerical results show that the proposed method has high macromodeling accuracy in time domain, and the modeling-error distribution in time domain can be efficiently controlled by the wavelet companding technique.