Calculations of the Gruneisen parameters of individual modes of vibration, of the average Gruneisen parameter, and of the temperature dependence of the elastic constants, of sodium iodide and potassium bromide have given reasonable agreement with experiment. The model used was a shell model, obtained from experimental measurements of the dispersion curves, extended in a simple way to include the anharmonicity. Calculations have also been made of the spectral functions of some of the normal modes propagating in the  direction. These show qualitative agreement with experiment in that the longitudinal optic modes are particularly temperature dependent. The results are used to discuss the validity and usefulness of a quasi-harmonic approximation in which the frequencies are those measured experimentally. The optical constants and the reflectivity of the crystals have also been calculated and are compared with experiment.