NOVELTY - A desulfurizer for fuel gas for a fuel cell containing at least one sulfur compound comprises: a first adsorption tank comprising first adsorber having a selective adsorption capacity for thiophene-based compounds; and second adsorption tank comprising second adsorber having a selective adsorption capacity for mercaptan-based compounds.    USE - For fuel gas for a fuel cell; for desulfurizing a fuel gas for a fuel cell containing sulfur compounds (claimed).    ADVANTAGE - The desulfurizer performs a more efficient, economical, and stable method of desulfurizing fuel gases used as fuel for fuel cells and containing various sulfur compounds, especially fuel gases containing thiophene-based compounds and mercaptan-based compounds in comparison to desulfurizer using a single adsorber. The desulfurizer uses separate adsorbers having selective adsorption capacity for a thiophene-based compound and a mercaptan-based compound in multiple stages to perform a more efficient and economical desulfurizing of a fuel gas to remove various sulfur compounds e.g. thiophene-based compounds and mercaptan-based compounds compared to a desulfurizer using a single adsorber. The desulfurizer removes the thiophene-based compound first using an Na-Y zeolite, which is relatively cheap, and then removes the mercaptan-based compound using an Ag-Y zeolite, which is relatively expensive.    DETAILED DESCRIPTION - INDEPENDENT CLAIMS are included for the following:    (1) a fuel processor for a fuel cell comprises the desulfurizer, a reformer and at least one carbon monoxide removal apparatus;    (2) a fuel cell system comprising the fuel processor and a fuel cell stack; and    (3) a method for desulfurizing a fuel gas for a fuel cell containing sulfur compounds involving: first removing thiophenes from the fuel gas using a first adsorber having a selective adsorption capacity for thiophene-based compounds; and then removing mercaptans that remain in the fuel gas using a second adsorber having an adsorption capacity for mercaptan-based compounds.