Relaxation time of lattice waves for a nonideal lattice has been obtained by using the $T$-matrix Green's-function method. The $T$ matrix for a defect which affects both the mass and the short-range interaction is taken into consideration for analyzing the irreducible representations of the point group pertaining to the perturbation. The resonances from ${F}_{1u}$, ${A}_{1g}$, and ${E}_{g}$ symmetry modes are discussed in detail for anion as well as cation impurities (${\mathrm{Tl}}^{+}$, ${\mathrm{Br}}^{\ensuremath{-}}$, ${\mathrm{I}}^{\ensuremath{-}}$, ${\mathrm{Cs}}^{+}$, ${\mathrm{Na}}^{+}$, and ${\mathrm{Ag}}^{+}$) in KCl crystals. A breathing-shell model with second-neighbor interactions is employed for a description of the host-lattice dynamics. Maxima are observed in the relative variation of $\ensuremath{\Delta}\frac{{C}_{L}(T)}{{C}_{L}^{0}}(T)$ with the temperature in all the systems except KCl:Na. These maxima are related to the appearance of quasilocal vibrations in the phonon spectrum of the host crystal due to introduction of impurities. The dips occuring in thermal conductivity curves appear to be due to the specialized modes of vibrations. In both studies the resonances appear at nearly the same frequencies in all the systems. The resonance frequencies observed by optical techniques are compared with the values obtained in the present work. The variation in force-constant changes does not affect the position of maxima in relaxation-rates-versus-frequency curves. The nature of the sodium impurity in KCl is discussed in detail. Three-phonon processes having different temperature dependences in the various temperature ranges have been used in the computations of thermal conductivity. The present theory shows reasonably good agreement with the experimental measurements on specific heat as well as with those on thermal conductivity of KCl doped with monovalent impurities.