Measurements were made of the absorption of the infrared-active local mode of H− and D− substitutional impurities in CsBr and CsI from 5 to about 100 K. In CsBr, the T2 dependence of the half-width above about 30 K indicates the local mode is broadened by the Raman or scattering mechanism, while the constant low-temperature half-widths are characteristic of the decay of the local mode into three (D−) or four (H−) lattice phonons. The sidebands are weak, and are described well by the model of Bilz, Fritz, and Strauch, in which the polarizability of the impurity is important. The resultant lattice density of states for CsBr is in good agreement with that calculated by Karo and Hardy using a model with the deformation dipoles on anions only. The main absorption peak in CsI was not Lorentzian, but no origin for the unresolved structure was found. The phonon density of states deduced from the sidebands in CsI agrees reasonably well with Karo and Hardy's calculated curve.