A fuel cell system, comprising: a fuel cell including an anode to which an anode gas is supplied and a cathode to which a cathode gas is supplied; a reformer for forming the anode gas by reforming a source gas; a source gas passage for supplying the source gas to the reformer; a gas conveying source provided at the source gas passage and supplying the source gas to the reformer via the source gas passage; a desulfurizer (100, 200) provided at the source gas passage for desulfurizing the source gas; a sensor detecting a physical quantity related to a water vapor included in the source gas directly or indirectly; and a control portion configured to execute a determination processing for determining whether a replacement of the desulfurizer (100, 200), or a desulfurization agent contained in the desulfurizer is necessary on the basis of the physical quantity related to the water vapor included in the source gas during an electric power generating operation of the fuel cell system; wherein the control portion is configured to not execute the determination processing when temperature at the desulfurizer is lower than a first predetermined temperature (Tx); and wherein the control portion is configured to not execute the determination processing at at least one of following cases: (i) at a warm-up mode at which the fuel cell system raises temperature of the reformer and/or the fuel cell before starting the electric power generating operation although the electric power generating operation is not performed; and (ii) when the source gas does not flow in the source gas passage. a fuel cell including an anode to which an anode gas is supplied and a cathode to which a cathode gas is supplied; a reformer for forming the anode gas by reforming a source gas; a source gas passage for supplying the source gas to the reformer; a gas conveying source provided at the source gas passage and supplying the source gas to the reformer via the source gas passage; a desulfurizer (100, 200) provided at the source gas passage for desulfurizing the source gas; a sensor detecting a physical quantity related to a water vapor included in the source gas directly or indirectly; and a control portion configured to execute a determination processing for determining whether a replacement of the desulfurizer (100, 200), or a desulfurization agent contained in the desulfurizer is necessary on the basis of the physical quantity related to the water vapor included in the source gas during an electric power generating operation of the fuel cell system; wherein the control portion is configured to not execute the determination processing when temperature at the desulfurizer is lower than a first predetermined temperature (Tx); and wherein the control portion is configured to not execute the determination processing at at least one of following cases: (i) at a warm-up mode at which the fuel cell system raises temperature of the reformer and/or the fuel cell before starting the electric power generating operation although the electric power generating operation is not performed; and (ii) when the source gas does not flow in the source gas passage. (i) at a warm-up mode at which the fuel cell system raises temperature of the reformer and/or the fuel cell before starting the electric power generating operation although the electric power generating operation is not performed; and (ii) when the source gas does not flow in the source gas passage.