Measurements of the far infrared absorption due to In+ and Tl+ impurities in CsBr and CsI single crystals yielded low frequency resonances with narrow linewidths at 11.0 cm−1 in CsBr:In+, 12.0 cm−1 in CsI:In+, 14.1 cm−1 in CsI:Tl+, and 16.95 cm−1 in CsBr:Tl+. The frequencies of the resonant band modes in the Tl+ doped crystals shift to higher values with increasing temperature. Using a model of the perturbed crystal which involves the mass defect and the change of the central force constants between the defect and its eight nearest neighbours, the force constant change is fitted to the various resonance frequencies. The resulting linewidths are compared with the experimentally determined values.