NOVELTY - The system (10) has electric conductivity meter (164) for measuring electric conductivity of water inside ion exchanger (78). A control device (22) controls the amount of electrical energy generated in fuel cell stack (28). An electric conductivity comparing unit (194) compares the electric conductivity measured by meter with predetermined electric conductivity range. An ion exchange environment determining unit (196) arbitrarily determines whether or not air is mixed into exchanger and whether or not ion exchange efficiency of the exchanger is degraded, based on comparison result.    USE - Fuel cell system installed in vehicle, used for stationary applications.    ADVANTAGE - The system arbitrarily determines whether or not the air has been mixed into the ion exchanger, and determine whether or not the ion exchange efficiency of the ion exchanger has been degraded, by using the electric conductivity meter with a simple and economical structure, so that the reduction in the number of steps of maintenance operation is achieved easily. The mixing of the air into water is detected easily with a simple and economical structure, so that the degradation of the performance of the pure water pump due to air entailment, oxidation of reforming catalyst due to mixing of the air into the reformer, and instability of power generation voltage of the fuel cell due to carbon deposition on the electrodes can be suppressed effectively. The power generation of the fuel cell stack is continued in the case where the electric conductivity is normal, so that the occurrence of problems related to water is suppressed and the improvement in durability of fuel cell system is achieved suitably. The number of components used in fuel cell system is reduced. The mixing of air into water is suppressed effectively. The electric conductivity of the water passed through the ion exchange resin is measured so as to detect the stagnation of the air and degradation of the ion exchange efficiency. The air can be discharged suitably. The ion exchange is performed reliably to achieve improvement in the ion exchange efficiency.    DETAILED DESCRIPTION - An INDEPENDENT CLAIM is included for the method for controlling fuel cell system.    DESCRIPTION OF DRAWING(S) - The drawing shows a block diagram of the fuel cell system.    Fuel cell system (10)    Control device (22)    Fuel cell stack (28)    Ion exchanger (78)    Electric conductivity meter (164)    Electric conductivity comparing unit (194)    Ion exchange environment determining unit (196)