Strontium and calcium amide are ionic compounds crystallizing in a tetragonally distorted anatase structure type. They include asymmetrically charged amide ions (NH2-/ND2-) which resemble water molecules in their structure and in their charge distribution. Bq means of temperature-dependent X-ray scattering measurements an anomalous thermal expansion was observed for both compounds (295 K for Sr(ND2)(2), 370 K for Ca(ND2)(2)). Fourier analyses based on high-resolution neutron powder diffraction experiments carried out in a large temperature range show especially for the deuterium atoms a remarkably large, anisotropic spatial distribution of the probability density function. It is caused by strongly anisotropic librations of the amide ions. The amplitudes of their normal librations were analyzed using a rigid-body model to parametrize the atomic mean-square displacements of the atoms belonging to the amide ions. They can be described as composed of strong rocking librations with weak temperature dependence and a weak wagging libration with strong temperature dependence.