A rotor run-up or run-down process provide more useful information for modal analysis than normal operation conditions. A traditional difficulty associated with rotor run-up or run-down analysis is the non-stationary nature of vibration data. This paper compares Short-Time Fourier Transform (STFT) and the wavelets analysis in these non-stationary signal analyses. An Adaptive Wavelet Analysis (AWT) is proposed to analyze these signals. Although simulations and experiments in a simple rotor-bearing system show that both STFT and AWT can be used to analyze non-stationary vibration signals in rotor dynamics, proposed AWT provides better results than STFT analysis. From the amplitude-frequency curve obtained by AWT, the modal frequency and damping ratio are calculated. This paper also analyzes the characteristics of signals when the shaft touches the outer hoop in a run-up process. The AWT can give a good result in this complex dynamic analysis of the touching process.