To assess the performance of damping augmentation strategies, accurate and reliable nonlinear damping identification techniques are needed. The transient response of a single-degree-of-freedom system having either nonlinear coulomb or quadratic damping is considered. Two analyses for identifying damping from transient test data are evaluated: an analysis based on a periodic Fourier series decomposition and a Hilbert-transform-based technique. Analytical studies for a spectrally isolated mode are used to determine the effects of block length, noise, and error in identified modal frequency on the accuracy of these techniques. The effect of a mode that is spectrally close to the primary mode of interest is also assessed. The primary mode has either coulomb or quadratic damping, and the spectrally close mode is either undamped or has a specified viscous damping level. A comprehensive evaluation of the effects of close mode amplitude, frequency, and damping level is performed. A classifier is also developed to identify the dominant damping mechanism in a signal of unknown composition, based on minimizing the mean square error between the predicted and identified envelope signals.