Fire-extinguishing system in an air filter system has an inlet chamber and an outlet chamber with a filter wall therebetween. The system includes a first and second sensor, a first and second fire extinguisher, and a control unit, the first sensor and the first extinguisher being disposed in the inlet chamber, the second extinguisher in an outlet chamber and the second sensor being disposed in an outlet of the outlet chamber. The control unit is connected to the first and second sensors, and to the first and second extinguishers. The control unit records a first and second fire-detection signal in the inlet chamber and the outlet, respectively; compares the first and second signals to an associated threshold value for fire; determines at which location within the inlet and outlet chamber the fire is burning, depending on the comparison; selects which of the first and at least one second extinguisher is located near the determined position, and activates one or more selected extinguishers.