NOVELTY - The apparatus (1) has a measurement unit to measure flow volume of gas to be de-sulfurized. Estimation unit estimates accumulating adsorption amount of sulfur content in desulfurization catalyst (11) from integration value measured by measurement unit, and updates residual amount of sulfur content in desulfurization catalyst. Estimation unit estimates that adsorption remaining power of sulfur content in desulfurization catalyst is below first predetermined value, when gas to be de-sulfurized having remaining-adsorptivity reducer level is contacted with desulfurization catalyst.    USE - Desulfurizing apparatus for de-sulfurizing gas to be de-sulfurized such as source gas, of fuel cell system (claimed).    ADVANTAGE - The lifetime of the desulfurization catalyst is estimated according to the adsorption remaining power fall substance level of gas to be de-sulfurized, and the capability of desulfurization catalyst is utilized effectively, so that the occurrence of breakthrough is prevented reliably.    DETAILED DESCRIPTION - The apparatus has a control unit that adjusts the contact conditions of gas to be de-sulfurized and desulfurization catalyst, so that the residual amount is adsorbed until reaching second predetermined value. A heating unit heats the said desulfurization catalyst. A contact avoidance unit avoids the contact to desulfurization catalyst of gas positioned by gas flow path to to-be-de-sulfurized gas. The contact avoidance unit is controlled, so that the adsorption remaining power of sulfur content in desulfurization catalyst is not permit the contact to desulfurization catalyst of gas. INDEPENDENT CLAIMS are included for the following:    (1) a desulfurization method involves measuring flow volume of gas to be de-sulfurized. The accumulating adsorption amount of sulfur content in desulfurization catalyst is estimated from the integration value measured by measurement unit, and the residual amount of sulfur content in desulfurization catalyst is updated. The estimation is performed to check that adsorption remaining power of sulfur content in desulfurization catalyst is below first predetermined value, when gas to be de-sulfurized having remaining-adsorptivity reducer level is contacted with desulfurization catalyst; and    (2) a fuel cell system has a modifier for modifying the gas de-sulfurized with desulfurizing apparatus to the reformed gas having hydrogen as a main component. A fuel cell introduces and electric-power-generates the oxidizing agent gas containing oxygen and reformed gas.    DESCRIPTION OF DRAWING(S) - The drawing shows a schematic block diagram of the desulfurizing apparatus. (Drawing includes non-English language text)    Desulfurizing apparatus (1)    Desulfurization catalyst (11)    Dew point hygrometer (21)    Flowmeter (22)    Fuel cell system (100)