Flexible metal-organic framework (MOF) compounds can exhibit very pronounced structural changes, which may be favorable for gas storage and gas separation applications. The noble gases xenon and krypton are increasingly important for both research and applications. Therefore, separation approaches with lower energy consumption are of great interest. In the present paper, the adsorption of pure xenon and krypton as well as their mixture by the flexible gate pressure MOFs is investigated using in situ high-pressure ¹²⁹Xe NMR spectroscopy and volumetric gas adsorption in combination with density-functional theory (DFT) calculations. The chosen model MOF compound DUT-8(Ni) can be synthesized as a flexible or rigid structure by tuning the crystallite size. This allows us to discriminate possible effects exerted by the framework flexibility from influences of structure and composition.