(57) A ventilating system for a building with several enclosed spaces, each having at least one automatically controlled ventilating device which communicates with the surroundings of the building and, depending on the pressure difference over the ventilating device, passes a specific constant throughput, and having a central mechanical exhaust device with a controllable ventilator, in which system per time block a programmable control unit controls the amount of ventilating air per space depending on a stated number of persons present in this space during that time block by controlling the supply devices and the ventilator, and in which system further a sensor placed near the ventilator is present, with which sensor the amount of air drawn in by the ventilator is to be determined, depending on which a control signal is to generated with the control unit, which control signal controls the number of revolutions of the ventilator such that, depending on the total number of persons stated to be present in the building, a constant amount of air is exhausted.