Abstract The structure of Xe overlayers on MgO powder in the temperature range 20 ⪯ T ⪯ 130 K at coverages from 0.6 to 2.0 monolayers has been investigated by means of X-ray diffraction. In addition, Kr on MgO has been investigated at a coverage of 0.8 monolayers. The coverage was calibrated by adsorption isotherm measurements. In both cases the structure of the adsorbate is triangular and hence incommensurate to the underlying square symmetry of the MgO(100) surface. The existence of a two-dimensional triple point temperature and regions of solid-gas and solid-liquid coexistence are deduced from the Xe diffraction patterns. In both adsorbates the long range order is disturbed due to the frustration arising from the difference between the adsorbate and substrate symmetry.