Noise-cancelling headphones comprising: - an electro-acoustic transducer placed in a sound reproduction cavity; - at least one noise-canceling processing chain (30, 40) comprising: - a microphone (31, 41) to capture ambient sound; - a noise-canceling filter (34, 44) to process the signal from the microphone (31, 41) to produce a noise-canceling signal; - means (18, 20) for applying the noise-canceling signal to drive the electro-acoustic transducer, wherein, for the or each noise-canceling processing chain (30, 40), the noise cancelling processing filter (34, 44) comprises in series: - a stabilisation filter (34A, 44A) whose transfer function is equal to the inverse (HFBcorr, HFFcorr) of the transfer function of a processed secondary path (Plant FB, Plant FF), and - a noise cancellation filter (34B, 44B) whose transfer function is a noise cancellation transfer function (HFB2, HFF2), the secondary path being formed between the electro-acoustic transducer and the user's eardrum, and the transfer function of the processed secondary path (Plant FB, Plant FF) being the predetermined transfer function of the secondary path combined with the transfer functions of all the components providing processing from the microphone (31, 41) up to the transducer in the noise-cancellation processing chain (30, 40), except for the noise-canceling processing filter (34, 44), wherein the headphones comprises an external noise-cancellation processing chain among said at least one noise-canceling processing chain (30, 40) having the microphone to capture ambient sound, this microphone being an external microphone placed in the sound reproduction cavity; and in the external noise-cancellation processing chain, the noise cancellation transfer function is equal to the opposite of the quotient of the predetermined transfer function corresponding to the passive attenuation of the cavity and the predetermined transfer function between the outer envelope of the cavity and the external microphone. - an electro-acoustic transducer placed in a sound reproduction cavity; - at least one noise-canceling processing chain (30, 40) comprising: - a microphone (31, 41) to capture ambient sound; - a noise-canceling filter (34, 44) to process the signal from the microphone (31, 41) to produce a noise-canceling signal; - a microphone (31, 41) to capture ambient sound; - a noise-canceling filter (34, 44) to process the signal from the microphone (31, 41) to produce a noise-canceling signal; - means (18, 20) for applying the noise-canceling signal to drive the electro-acoustic transducer, wherein, for the or each noise-canceling processing chain (30, 40), the noise cancelling processing filter (34, 44) comprises in series: - a stabilisation filter (34A, 44A) whose transfer function is equal to the inverse (HFBcorr, HFFcorr) of the transfer function of a processed secondary path (Plant FB, Plant FF), and - a noise cancellation filter (34B, 44B) whose transfer function is a noise cancellation transfer function (HFB2, HFF2), - a stabilisation filter (34A, 44A) whose transfer function is equal to the inverse (HFBcorr, HFFcorr) of the transfer function of a processed secondary path (Plant FB, Plant FF), and - a noise cancellation filter (34B, 44B) whose transfer function is a noise cancellation transfer function (HFB2, HFF2), the secondary path being formed between the electro-acoustic transducer and the user's eardrum, and the transfer function of the processed secondary path (Plant FB, Plant FF) being the predetermined transfer function of the secondary path combined with the transfer functions of all the components providing processing from the microphone (31, 41) up to the transducer in the noise-cancellation processing chain (30, 40), except for the noise-canceling processing filter (34, 44), wherein the headphones comprises an external noise-cancellation processing chain among said at least one noise-canceling processing chain (30, 40) having the microphone to capture ambient sound, this microphone being an external microphone placed in the sound reproduction cavity; and in the external noise-cancellation processing chain, the noise cancellation transfer function is equal to the opposite of the quotient of the predetermined transfer function corresponding to the passive attenuation of the cavity and the predetermined transfer function between the outer envelope of the cavity and the external microphone.