Condition monitoring of epicyclic gearboxes through vibration signature analysis, with particular focus on time domain methods and the use of adaptive filtering techniques for the purpose of signal enhancement, is the central theme of this work. Time domain filtering methods for the purpose of removal of random noise components from periodic, but not necessarily stationary or cyclostationary, signals are developed. Damage identification is accomplished through vibration signature analysis by nonstationary timefrequency methods, belonging to Cohen’s general class of time-frequency distributions, strictly based in the time domain. Although a powerful and commonly used noise reduction technique, synchronous averaging requires alternate sensors in addition to the vibration pickup. For this reason the use of time domain techniques that employ only the vibration data is investigated. Adaptive filters may be used to remove random noise from the nonstationary signals considered. The well-known Least Mean Squares algorithm is employed in an adaptive line enhancer configuration. To counter the much discussed convergence difficulties that are often experienced when the least mean squares algorithm is applied, a new unconditionally convergent algorithm based on the spherical quadratic steepest descent method is presented. The spherical quadratic steepest descent method has been shown to be unconditionally convergent when applied to a quadratic objective function. Time-frequency methods are succinctly employed to analyse the vibration signals simultaneously in the time and frequency domains. Transients covering a wide frequency range are a clear and definite indication of impacting events as gear teeth mate, and observation of such events on a timefrequency distribution are used to indicate damage to the transmission. The pseudo Wigner-Ville distribution and the Spectrogram, both belonging to Cohen’s general class of time-frequency distributions are comparatively used to the end of damage identification. It is shown that an unconditionally convergent adaptive filtering technique used in conjunction with time-frequency methods can indicate a damaged condition in an epicyclic gearbox, where the non-adaptively filtered data did not present clear indications of damage.