Accurate integrated intensities for the Bragg reflexion of neutrons by crystals of ZnS and ZnTe have been measured at room temperature. Measurements were made at a number of wavelengths and corrections were made for extinction and thermal diffuse scattering. The experimental data show contributions arising from third-order anharmonic thermal vibration of the ions. However, it is shown that, although both types of ion have a tetrahedral site symmetry and can thus give rise to such anharmonic contributions, only a single anharmonicity parameter can be determined from the neutron measurements. The magnitude of the anharmonicity parameter is similar to that obtained for the fluorine ions in CaF2, SrF2 and BaF2. The nuclear scattering amplitude of zinc was refined to bzn = 0.569 (2) × 10−12 cm, assuming a value for the nuclear scattering amplitude of sulphur of bs = 0.2847 (1) × 10−12 cm.