A method for operating a binaural hearing system comprising a first and a second hearing device (1, 1') operationally interconnected by means of a bidirectional link and each having a microphone arrangement (2, 2') and an electrical-to-mechanical output converter (3, 3'), the method comprising the steps of: - capturing a first audio signal with the microphone arrangement of the first hearing device being worn at one ear of a user; - capturing a second audio signal with the microphone arrangement of the second hearing device being worn at the other ear of the user; - determining a level of a first wind noise based on the first audio signal; - determining a level of a second wind noise based on the second audio signal; - sending • an ancillary signal derived from the first audio signal from the first hearing device to the second hearing device if the level of the second wind noise exceeds the level of the first wind noise by a pre-set threshold value (Th min), or • an ancillary signal derived from the second audio signal from the second hearing device to the first hearing device if the level of the first wind noise exceeds the level of the second wind noise by the pre-set threshold value (Th min); and - providing • a mixture of a first output signal derived from the ancillary signal received from the second hearing device and of a second output signal derived from the first audio signal to the electrical-to-mechanical output converter of the first hearing device if the level of the first wind noise exceeds the level of the second wind noise by the pre-set threshold value (Th min), or • a mixture of a first output signal derived from the ancillary signal received from the first hearing device and of a second output signal derived from the second audio signal to the electrical-to-mechanical output converter of the second hearing device if the level of the second wind noise exceeds the level of the first wind noise by the pre-set threshold value (Th min), wherein low-pass filtering is applied to derive the ancillary signal and/or the first output signal, and wherein high-pass filtering is applied to derive the second output signal. - capturing a first audio signal with the microphone arrangement of the first hearing device being worn at one ear of a user; - capturing a second audio signal with the microphone arrangement of the second hearing device being worn at the other ear of the user; - determining a level of a first wind noise based on the first audio signal; - determining a level of a second wind noise based on the second audio signal; - sending • an ancillary signal derived from the first audio signal from the first hearing device to the second hearing device if the level of the second wind noise exceeds the level of the first wind noise by a pre-set threshold value (Th min), or • an ancillary signal derived from the second audio signal from the second hearing device to the first hearing device if the level of the first wind noise exceeds the level of the second wind noise by the pre-set threshold value (Th min); and • an ancillary signal derived from the first audio signal from the first hearing device to the second hearing device if the level of the second wind noise exceeds the level of the first wind noise by a pre-set threshold value (Th min), or • an ancillary signal derived from the second audio signal from the second hearing device to the first hearing device if the level of the first wind noise exceeds the level of the second wind noise by the pre-set threshold value (Th min); and - providing • a mixture of a first output signal derived from the ancillary signal received from the second hearing device and of a second output signal derived from the first audio signal to the electrical-to-mechanical output converter of the first hearing device if the level of the first wind noise exceeds the level of the second wind noise by the pre-set threshold value (Th min), or • a mixture of a first output signal derived from the ancillary signal received from the first hearing device and of a second output signal derived from the second audio signal to the electrical-to-mechanical output converter of the second hearing device if the level of the second wind noise exceeds the level of the first wind noise by the pre-set threshold value (Th min), wherein low-pass filtering is applied to derive the ancillary signal and/or the first output signal, and wherein high-pass filtering is applied to derive the second output signal. • a mixture of a first output signal derived from the ancillary signal received from the second hearing device and of a second output signal derived from the first audio signal to the electrical-to-mechanical output converter of the first hearing device if the level of the first wind noise exceeds the level of the second wind noise by the pre-set threshold value (Th min), or • a mixture of a first output signal derived from the ancillary signal received from the first hearing device and of a second output signal derived from the second audio signal to the electrical-to-mechanical output converter of the second hearing device if the level of the second wind noise exceeds the level of the first wind noise by the pre-set threshold value (Th min),