The problem of parameter estimation is considered for the case of mathematical models for polymer electrolyte membrane fuel cells (PEMFCs). An algorithm for nonlinear least squares constrained by partial differential equations is defined and applied to estimate effective membrane conductivity, exchange current densities and oxygen diffusion coefficients in a one-dimensional PEMFC model for transport in the principal direction of current flow. Experimental polarization curves are fitted for conventional and low current density PEMFCs. Use of adaptive mesh refinement is demonstrated to increase the computational efficiency. (c) 2005 Elsevier B.V. All rights reserved.