TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Components: The adsorber of the first adsorption tank is an Na-Y zeolite. The adsorber of the second adsorption tank is an Ag-Y zeolite. The Si/Al ratio of the Na-Y and Ag-Y zeolite is 2-5. The Na/Al ratio of the Na-Y zeolite is 0.1-1. The Ag/Al ratio of the Ag-Y zeolite is 0.2-0.7. The adsorber of the first adsorption tank is prepared by pretreating a Na-Y zeolite at 350-450degreesC for 3-5 hours in air. The Ag-Y zeolite is formed by pretreating an Na-Y zeolite at 350-450degreesC for 3-5 hours in air and then ion-exchanging the pretreated Na-Y zeolite in an Ag precursor solution at 25-30degreesC for 30 minutes t0 2 hours. The guard bed comprises at least one material selected from a zeolite, silica gel, and activated carbon.    TECHNOLOGY FOCUS - INSTRUMENTATION AND TESTING - Preferred Desulfurizer: The desulfurizer further comprises a guard bed in front of the first and/or second adsorption tanks to remove moisture and impurities in the fuel gas; an indicator after the second adsorption tank to indicate the concentration of a sulfur compound in the desulfurized fuel gas.    TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Components: The first adsorption tank is in a first section of the desulfurizer and the second adsorption tank is in a second section of the desulfurizer downstream from the first section. The first adsorption tank is in an upper section of the desulfurizer and the second adsorption tank is in a lower section of the desulfurizer. The first adsorber has a selective adsorption capacity for at least one compound selected from thiophenol, alkylthiophene, and benzothiophene (preferably tetrahydrothiophene). The alkylthiophene comprises at least one material selected from 2-methylthiophene, 3-methylthiophene, ethylthiophene, dimethyl thiophene, trimethylthiophene, and tetrahydrothiophene (THT). The benzothiophene comprises at least one material selected from benzothiophene, dibenzothiophene, methylbenzothiophene, and dimethylbenzothiophene. The second adsorber has a selective adsorption capacity for at least one compound selected from 1-ethanethiol, 1-propanethiol, 2-propanethiol, 2-butanethiol, tert-butyl mercaptan (TBM), 2-methyl-2-propanethiol, pentanethiol, hexanethiol, heptanethiol, octanethiol, nonanethiol, and thiophenol (preferably tertiarybutylmercaptan). In the method, the fuel gas is a city gas containing thiophenes and mercaptans. Preferred Method: In the method, the removing of thiophenes and the removing of mercaptans are performed at 0-50 degreesC or 0.5-2.5 atmosphere. The method is carried out by passing the fuel gas through a first adsorption tank comprising the first adsorber; and then passing the fuel gas through a second adsorption tank comprising the second adsorber. EXAMPLE - A two-step desulfurizer was prepared by charging a first adsorption tank on an upper section of the two-step desulfurizer with Na-Y zeolite (0.15 g) (ratio of Si/Al: 2.8, ratio of Na/Al: 1) and a second adsorption tank on a lower section of the two-step desulfurizer with Ag-Y zeolite (0.15 g) (ratio of Si/Al: 2.8, ratio of Ag/Al: 0.7). The Na-Y zeolite was pretreated at 400degreesC for 4 hours in air. The Ag-Y zeolite was prepared by pretreating an Na-Y at 400degreesC for 4 hours in air and then ion-exchanging the pretreated zeolite by impregnating the pretreated zeolite in an Ag precursor solution for 1 hour at 27degreesC. Methane gas containing tetrahydrothiophene (THT) (70 ppm) and tert-butyl mercaptan (TBM) (30 ppm) was passed through the two-step desulfurizer, formed of the first adsorption tank and the second adsorption tank, at 55 cm3/minuts at room temperature. Concentrations of sulfur in the effluent from the desulfurizer were measured according to time, and the results were as follows: TBM, which represents unadsorbed sulfur, was detected in the effluent from the desulfurizer 30 hours after the experiment began.