The disturbed trajectories of power system usually are of non-stationary oscillation characteristics， which can not be represented by equilibrium point eigenvalues. Therefore， the concepts of time-variant oscillation modes and trajectory eigenvalues are put forward. The way to calculate the instantaneous frequency and damping factor is also given. Time sequence of oscillation modes， composed of the eigenvalues in sliding windows along the trajectory and derived from wavelet ridge methods， clearly shows the influence of the non-linearity and time-variation on low frequency oscillations. By tracing the local maximum points of wavelet transform， this method overcomes the inapplicability of the Prony and Fourier algorithms to time-variant systems. However， the wavelet transform can not deal with fast time-variation cases because it treats the dynamics within a window as a stationary oscillation. For such cases， time sequence of trajectory eigenvalues at a series of moments should be developed.