There are four basic classes of methods of analyzing exponential decay curves: graphical methods, iterative fitting methods, algebraic fitting methods, and transform methods. Representative types of all these methods are examined in detail as to their approach to computing exponents and their theoretical strengths and weaknesses. A comparison is made of the methods on simulated data and a survey of the reported accuracy of the methods in the literature is used to illustrate these strengths and weaknesses. Consequently, a three-method sequential identification scheme utilizing the graphical curve-peeling method, the DFT (Discrete Fourier Transform) deconvolution method [a new method developed for this study], and the iterative weighted nonlinear leastsquares method is developed for application to real physical data. A series of four examples of the application of the sequential identification scheme is made for physiological data containing from two to four exponents. The intrinsic difficulties of exponential analysis are illustrated, and the utility of the sequential identification scheme is shown.