This paper describes the analysis of photon correlation spectroscopy decay curves by a significant new method based on the fitting of sums of positive exponentials by the S-exponential sum fitting method. The method fits a positive exponential sum to a given data set providing a best weighted least squares fit. No initial setting of any of the parameters is required and the number of exponential coefficients does not have to be preset in the program but is determined by the number of components apparent above the noise level. Results will be discussed for application in scattering systems which may be single or multiple component. Systems generating single, double or multiple exponential decay functions derived from computer simulation or photon correlation exneriments are considered and fitting analysis with varying noise levels.