The dynamic behaviour of high-performance mechanical systems such as robots is strongly influenced by the characteristics of the link joints. Joint backlash as a result of wear due to severe stress imposed on the transmission system degrades the robot performance. This paper presents a systematic methodology to diagnose the joint-backlash of a robot by monitoring its vibration response during normal operations. To indicate the reversal of motion of a robot link, and to characterise the spectral patterns of vibration signatures, non-stationary time-frequency analysis algorithms have been employed, which illustrate the signature in a simultaneous time-frequency plane. Significant features are extracted from time domain analysis (probability density moments), and from time-frequency domain analysis (local energy calculations). Artificial neural networks are used as tools for pattern recognition. Experimental results show that the proposed techniques can analyse single-joint backlash quantitatively. Moreover, the described methods also allow to single out backlash in the individual joints in case of multiple-joint backlash.