Requiring quite wide sliding windows， signal processing techniques for extracting oscillation-mode information are applicable for neither fast time-varying systems nor strong nonlinear systems. To overcome the shortcomings， a method to calculate time-varying eigenvalues series is proposed based on the piecewise-linearized system models along the disturbed trajectories. Eigenvalue calculation is performed at the beginning of every time step for numerical integration. Furthermore， the piecewise-linearized dynamic equations are mapped into a series of time-varying one machine infinite bus（OMIB） systems and the oscillation mode within each integration-step can be identified with analytical formulas of extended equal-area criterion（EEAC）. This makes the estimation of trajectory eigenvalues not only quickly but also accurately. The method is applied to a 3-machine 9-node test system and the effects of nonlinear non-autonomous factors on the eigenvalues are investigated.