Air exchange system for the ventilation of at least one room of a building, having the following features: - at least an air exchange device, which comprises a casing, an electric supply air fan arranged in the casing for the transport of a supply air flow from the outer face to the inner face of the building,an electric exhaust air fan arranged in the casing for the transport of an exhaust air flow from the inside to the outside of the building, and a heat exchanger, the supply air flow flowing through the heating side or, respectively, the cooling side and the exhaust air flow flowing through the cooling side or, respectively, the heating side of the heat exchanger, - at least one outdoor air humidity sensor (25; 32) arranged in the casing, in particular next to an exhaust air inlet opening of the casing for measuring the air humidity of the air located at the outside of the building, - at least one indoor temperature sensor (28; 35) arranged in the casing, in particular next to an exhaust air inlet opening of the casing, for measuring the air temperature at the inside of the building, - a computation unit, which is connected with the outdoor air humidity sensor (25; 32) and with the indoor temperature sensor (28; 35), for the computation of the expected relative air humidity of the air transported to the inside of the building from the measured values of the outdoor air humidity sensor (25; 32) and the indoor temperature sensor (28; 35), - a control unit connected to the computation unit, which is operably connected with the supply air fan, such that the supply air fan assumes a first ventilation operating mode, in which the rotational frequency of the supply air fan is equal to zero or is configured as a minimum ventilation rotation frequency, if the expected relative humidity of the supply air flow exceeds a pre-determined first maximum value or if the expected relative humidity of the supply air flow falls below a pre-determined first minimum value, and/or such that the supply air fan assumes a second ventilation operation mode, in which the rotation frequency of the supply air fan is greater than the rotation frequency of the first ventilation operation mode, if the expected relative air humidity of the supply air flow falls below a pre-determined second maximum value, or if the expected relative humidity of the supply air flow exceeds a pre-determined second minimum value. - at least an air exchange device, which comprises a casing, an electric supply air fan arranged in the casing for the transport of a supply air flow from the outer face to the inner face of the building,an electric exhaust air fan arranged in the casing for the transport of an exhaust air flow from the inside to the outside of the building, and a heat exchanger, the supply air flow flowing through the heating side or, respectively, the cooling side and the exhaust air flow flowing through the cooling side or, respectively, the heating side of the heat exchanger, - at least one outdoor air humidity sensor (25; 32) arranged in the casing, in particular next to an exhaust air inlet opening of the casing for measuring the air humidity of the air located at the outside of the building, - at least one indoor temperature sensor (28; 35) arranged in the casing, in particular next to an exhaust air inlet opening of the casing, for measuring the air temperature at the inside of the building, - a computation unit, which is connected with the outdoor air humidity sensor (25; 32) and with the indoor temperature sensor (28; 35), for the computation of the expected relative air humidity of the air transported to the inside of the building from the measured values of the outdoor air humidity sensor (25; 32) and the indoor temperature sensor (28; 35), - a control unit connected to the computation unit, which is operably connected with the supply air fan, such that the supply air fan assumes a first ventilation operating mode, in which the rotational frequency of the supply air fan is equal to zero or is configured as a minimum ventilation rotation frequency, if the expected relative humidity of the supply air flow exceeds a pre-determined first maximum value or if the expected relative humidity of the supply air flow falls below a pre-determined first minimum value, and/or such that the supply air fan assumes a second ventilation operation mode, in which the rotation frequency of the supply air fan is greater than the rotation frequency of the first ventilation operation mode, if the expected relative air humidity of the supply air flow falls below a pre-determined second maximum value, or if the expected relative humidity of the supply air flow exceeds a pre-determined second minimum value.