Combination of a ventilating device for a building with a further ventilating device, - wherein the ventilating devices each have a ventilating channel which connects together a first and a second ventilating opening (5, 6) of the respective ventilating device, - wherein the respective ventilating channel has a number of sections which are flowed through in succession by an air flow flowing through the respective ventilating channel, - wherein the sections each have a heat store thermally coupled to the air flow flowing through the respective section of the ventilating channel of the respective ventilating device, - wherein the ventilating device does not have a fan device and the further ventilating device has a fan device, so that in operation of the ventilating device and the further ventilating device in the building the flow direction in the ventilating channel of the ventilating device without a fan device follows the flow direction in the ventilating channel of the ventilating device with a fan device, - wherein a control device is associated with the fan device of the further ventilating device, characterised in that - at least one sensor for air humidity and/or volatile organic compounds is associated with the further ventilating device, - the control device is in data connection with the sensor for feed of the senor signal detected by the sensor and - the control device has such a configuration that it operates the fan device in such a way that in the normal case the flow direction of the further ventilating device is inverted in each instance after expiry of a time limit, but sets a defined flow direction or a completely suppresses activation of the fan device if the control device on the basis of the sensor signal recognises an air humidity and/or concentration of the volatile organic compounds above a limit value. - wherein the ventilating devices each have a ventilating channel which connects together a first and a second ventilating opening (5, 6) of the respective ventilating device, - wherein the respective ventilating channel has a number of sections which are flowed through in succession by an air flow flowing through the respective ventilating channel, - wherein the sections each have a heat store thermally coupled to the air flow flowing through the respective section of the ventilating channel of the respective ventilating device, - wherein the ventilating device does not have a fan device and the further ventilating device has a fan device, so that in operation of the ventilating device and the further ventilating device in the building the flow direction in the ventilating channel of the ventilating device without a fan device follows the flow direction in the ventilating channel of the ventilating device with a fan device, - wherein a control device is associated with the fan device of the further ventilating device, characterised in that - at least one sensor for air humidity and/or volatile organic compounds is associated with the further ventilating device, - the control device is in data connection with the sensor for feed of the senor signal detected by the sensor and - the control device has such a configuration that it operates the fan device in such a way that in the normal case the flow direction of the further ventilating device is inverted in each instance after expiry of a time limit, but sets a defined flow direction or a completely suppresses activation of the fan device if the control device on the basis of the sensor signal recognises an air humidity and/or concentration of the volatile organic compounds above a limit value.