In order to improve the energy efficiency and compact structure, the dual-rotor structure including the low- pressure rotor and high-pressure rotor has been widely used in aero-engine. Misalignment is one of the most common faults in the dual-rotor system, which will causes malfunctions. It is a significant task for rotor dynamics personnel to monitor and detect faults in the dual-rotor system. In the paper, the dual-rotor vibration signals are applied to solve the fault identification problem by utilizing time-frequency techniques. Numerical simulations are carried out through finite element analysis of the dual-rotor system with misalignment fault. Two signal processing tools namely Short Time Fourier Transform (STFT) and Continuous Wavelet Transform are used to detect the misalignment fault and compared to evaluate their diagnosis performance. The effect of the addition of Signal to Noise (SNR) on three frequency techniques is presented. Experiments are carried out to obtain the vibration data of dual-rotor test rig and the results from the work show that the technique can be used for the monitoring of misalignment, which will have applications in the condition monitoring and maintenance of various types of rotating machinery.