Cengel and Boles discuss in their Thermodynamics textbook that the Carnot efficiency bound is not applicable to fuel cells, whereas some researchers have raised objection that maximum conversion efficiency of fuel cells is limited to the Carnot efficiency. We apply the conservation of energy and entropy balance equations to derive expressions for the maximum work of hydrogen-oxygen, hydrogen-air and methane-air fuel cells. We show that the theoretical efficiency of a fuel cell may exceed that of a Carnot engine operating between the same low and high temperatures. Contrary to past studies in that the efficiency of an ideal hydrogen fuel cell is shown to decline with temperature, the maximum efficiency is observed to first decrease with reactants temperature, then remains unaltered and finally rises. The lowest value of the maximum efficiency is found to be 79.3%, 75.7%, and 82.1% for hydrogen-oxygen, hydrogen-air and methane-air fuel cells, respectively. By increasing the stoichiometric coefficient of air, the efficiencies of both hydrogen-air and methane-air fuel cells monotonically increase and they approach the 100% limit at a stoichiometric coefficient of 7.2 and 9.8, respectively. It is shown that a Carnot engine whose heat is supplied by an isothermal combustor proposed in some past studies is not a correct means for comparison of the ideal performance of fuel cells and heat engines. (C) 2018 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.