Fuel cell systems and methods for controlling the operation of fuel cell assemblies included therein. In some embodiments, the fuel cell assemblies include a fuel processor and a fuel cell stack, and the fuel cell system includes a control system that controls the operation thereof based upon at least one variable associated therewith. In some embodiments, the variable is associated with the hydrogen (or other product) stream from the fuel processor. In some embodiments, the variable is the pressure of this stream. In some embodiments, the control system controls the operation of the fuel cell system to maintain the pressure of the hydrogen stream within one or more threshold values. In some embodiments, the control system controls the operation of the fuel cell system to maintain the pressure of the hydrogen stream within selected threshold values and to maintain the fuel cell stack's output voltage above a selected threshold.