For complex biological systems, conventional analysis of fluorescence intensity decay in terms of discrete exponential components cannot readily provide a true representation of the underlying fluorescence dynamics. We investigate an alternative nonparametric method for the analysis of time-resolved fluorescence data from biochemical and biological systems based on the expansion of fluorescence decay in a discrete Laguerre basis. We report that a unique Laguerre expansion can be found for fluorescence intensity decays of arbitrary form with convergence to a correct solution significantly faster than conventional multiexponential approximation methods. The Laguerre expansion coefficients are shown to be highly correlated with intrinsic fluorescence lifetimes and allow direct characterization of the fluorescence dynamics. A novel method for prediction of concentrations in mixtures of biochemical components using these coefficients is developed and successfully tested (prediction error <2%) using data from different mixtures of fluorescence lifetime standards. These findings suggest that the use of Laguerre expansion coefficients is a fast approach for the characterization and discrimination of complex biological systems such as tissues and cells, and that the method has potential for applications of fluorescence lifetime techniques to tissue diagnostics and imaging microscopy of living cells.