Fuel cell stack with integrated filter device

The fuel cell stack (1) consists of a number of fuel cells with a filter device for filtering an operating medium that is fed to the fuel cell stack with a filter (5) that is integrated into the fuel cell stack. The filter is inserted into an axial main line of the fuel cell stack. A gap is provided between the outer surface of the filter and the wall of the main line. An independent claim is also included for a method of operating a fuel cell stack.