NOVELTY - A fuel cell system comprises a first heating mechanism (77a) and second heating mechanism (77b) for supplying exhaust gas as heat source for respectively directly and indirectly heating a preliminary reformer; and a control mechanism for controlling the heating mechanisms to maintain the state of the preliminary reformer to have a predetermined reforming condition value. The fuel gas produced by the preliminary reformer is supplied to the anode. Water produced in power generation reaction of the electrolyte electrode assembly is used for reforming the fuel gas by steam reforming at the anode.    USE - For e.g. a vehicle.    ADVANTAGE - The preliminary reformer is directly heated by some of the exhaust gas and indirectly heated by the heat exchanger to which the remaining exhaust gas is supplied. By simply controlling the direct heating and indirect heating, the state of the preliminary reformer is maintained to have the predetermined reforming condition values reliably. The steam to carbon (S/C) ratio can be lowered down to the coking limit. The amount of supplied water is reduced. The capacity of the water supply power source, e.g. water pump, is reduced to effectively reduce the load of the fuel cell. Water produced in the power generation reaction is utilized in the reforming reaction at the anode and the amount of water supplied into the fuel cell system is reduced as a whole. The size of the water supply power source is reduced and the load of the fuel cell and the consumption amount of water are reduced.    DETAILED DESCRIPTION - A fuel cell system comprises a fuel cell stack (12) formed by stacking fuel cells each including an electrolyte electrode assembly and a separator, where the electrolyte electrode assembly includes an anode, a cathode and an electrolyte interposed between anode and cathode; a heat exchanger for heating an oxygen-containing gas to be supplied to the fuel cell stack; a preliminary reformer for reforming a mixed fuel of a raw fuel containing hydrocarbon and water vapor by steam reforming to produce a fuel gas; a first heating mechanism (77a) for supplying some of an exhaust gas discharged from the fuel cell stack after consumption in power generation reaction to the preliminary reformer as a heat source for directly heating the preliminary reformer; a second heating mechanism (77b) for supplying the remaining exhaust gas to the heat exchanger as a heat source for heating the oxygen-containing gas and supplying the heat generated in the heat exchanger to the preliminary reformer as a heat source for indirectly heating the preliminary reformer; and a control mechanism for controlling the first and second heating mechanisms to maintain the state of the preliminary reformer to have a predetermined reforming condition value. The fuel gas produced by the preliminary reformer is supplied to the anode. Water produced in power generation reaction of the electrolyte electrode assembly is used for reforming the fuel gas by steam reforming at the anode.    An INDEPENDENT CLAIM is also included for a method of operating a fuel cell system comprising    (A) supplying some of an exhaust gas discharged from the fuel cell stack after consumption in power generation reaction to the preliminary reformer as a heat source for directly heating the preliminary reformer;    (B) supplying the remaining exhaust gas to the heat exchanger as a heat source for heating the oxygen-containing gas and supplying the heat generated in the heat exchanger to the preliminary reformer as a heat source for indirectly heating the preliminary reformer;    (C) controlling the direct heating and the indirect heating of the preliminary reformer for maintaining the state of the preliminary reformer to have a predetermined reforming condition value; and    (D) supplying the fuel gas produced by the preliminary reformer to the anode for reforming the fuel gas by steam reforming at the anode using water produced in power generation reaction of the electrolyte electrode assembly.    DESCRIPTION OF DRAWING(S) - The figure shows a fuel cell system.    Fuel cell stack (12)    Fluid unit (14)    Casing (16)    First heating mechanism (77a)    Second heating mechanism (77b)    Inlet (102)    Outlet (122)    Temperature sensors (130a-130d)    Valve (132)