The far‐infrared conductivity spectra of the fast ion conductor β‐CuBr (683 K), of the mixed crystal Ag0.85Cu0.15Br (573 K), and of AgBr (573 K) are experimentally determined from transmittance and reflectivity data. The very‐far‐infrared absorption band typical of structurally disordered solid electrolytes is observed in both β‐CuBr and Ag0.85Cu0.15Br. The band is interpreted in terms of a large‐amplitude irregular local motion of the cations. In the case of β‐CuBr, calculated frequency spectra are compared to the experimental conductivity.