This paper proposes the use of the distribution of relaxation times (DRT) for the analysis of the dynamic behavior of hydrogen fuel-cells. With this aim it presents a new method to compute the DRT directly from electrochemical impedance spectroscopy (EIS) data. The method is formulated as a nonconvex complex domain optimization problem where each EIS spectra is approximated by a general fractional-order Legendre basis. The DRT is computed directly from the Legendre basis functions and validated against the experimental data. The method is tested with real EIS data collected from an hydrogen polymer electrolyte fuel-cell under different operating conditions and the results are discussed. © 2013 Elsevier B.V.