Abstract. The manifestation of phonon dispersion on frequency and temperature dependence of exciton damping is investigated theoretically for the models of crystal with the large and small exciton radii. The correlation between the dispersion and the frequency intervals with phonon absorption and emission is discussed for the exciton of TlBr, ZnS and some other crystals as examples. It is demonstrated that depending on frequency the dispersion results both in increase and reduction of the exciton damping. In addition, the intensity of exciton damping close to the peaks of phonon absorption and emission is varied. The change of the tendency of influence of dispersion on damping for some fixed frequency with temperature growing is noticed.