A binaural hearing aid system, comprising: - a left ITE hearing aid with an antenna facility; - a right ITE hearing aid with an antenna facility; - means for transmitting audio signals between the antenna facility of the left ITE hearing aid and the antenna facility of the right ITE hearing aid, - means for a binaural beamforming based on the natural directivity of the pinna and/or based on a head shadowing effect, and - means for an adaptive beamforming and/or means for noise reduction and/or means for head movement compensation, - wherein the antenna facility of each of the ITE hearing aids (42, 43) comprises: - an antenna arrangement (16, 36) with a coil core (22, 32) made of magnetically permeable material, and extending along a longitudinal axis, - a further electric hearing aid component (14, 34), which emits electromagnetic interference radiation, and - an at least partially planar shield (26, 37) made of magnetically permeable material, - wherein the shield (26, 37) is arranged between the antenna arrangement (16, 36) and the further hearing aid component (14, 34), wherein the shield (26, 37) is arranged transverse to the longitudinal axis of the coil core (22, 32) and wherein the shield (26, 37) is arranged at a distance of 50 to 150 micrometers from the coil core (22, 32). - a left ITE hearing aid with an antenna facility; - a right ITE hearing aid with an antenna facility; - means for transmitting audio signals between the antenna facility of the left ITE hearing aid and the antenna facility of the right ITE hearing aid, - means for a binaural beamforming based on the natural directivity of the pinna and/or based on a head shadowing effect, and - means for an adaptive beamforming and/or means for noise reduction and/or means for head movement compensation, - wherein the antenna facility of each of the ITE hearing aids (42, 43) comprises: - an antenna arrangement (16, 36) with a coil core (22, 32) made of magnetically permeable material, and extending along a longitudinal axis, - a further electric hearing aid component (14, 34), which emits electromagnetic interference radiation, and - an at least partially planar shield (26, 37) made of magnetically permeable material, - wherein the shield (26, 37) is arranged between the antenna arrangement (16, 36) and the further hearing aid component (14, 34), wherein the shield (26, 37) is arranged transverse to the longitudinal axis of the coil core (22, 32) and wherein the shield (26, 37) is arranged at a distance of 50 to 150 micrometers from the coil core (22, 32). - an antenna arrangement (16, 36) with a coil core (22, 32) made of magnetically permeable material, and extending along a longitudinal axis, - a further electric hearing aid component (14, 34), which emits electromagnetic interference radiation, and - an at least partially planar shield (26, 37) made of magnetically permeable material, - wherein the shield (26, 37) is arranged between the antenna arrangement (16, 36) and the further hearing aid component (14, 34), wherein the shield (26, 37) is arranged transverse to the longitudinal axis of the coil core (22, 32) and wherein the shield (26, 37) is arranged at a distance of 50 to 150 micrometers from the coil core (22, 32).