Metal-organic frameworks are promising candidates for selective separation processes such as CO, removal from methane (natural gas sweetening). Framework flexibility, that is, the ability of a MOF lattice to change its structure as a function of parameters like pressure, temperature, and type of adsorbed molecules, is only observed for some special compounds. The main question of our present work is: does framework flexibility influence the adsorption selectivity? As a direct quantitative method to monitor the adsorption of both, carbon dioxide and methane, we make use of high-pressure in situ C-13 NMR spectroscopy of (CO2)-C-13/(CH4)-C-13 gas mixtures. This method allows to distinguish between the two gases as well as between adsorbed molecules and the interparticle gas phase. Gas mixture adsorption is studied under isothermal conditions. The selectivity factor for CO, adsorption from CO2/CH4 mixtures is measured as a function of total gas pressure. The flexible material SNU-9 as well as the flexible and the nonflexible variant of DUT-8(Ni) are compared. Maximum selectivity factors for CO2 are observed for the flexible variant of DUT-8(Ni) in its open, large-pore state. In contrast, the rigid variant of DUT-8(Ni) and SNU-9 especially in its intermediate state exhibits lower adsorption selectivity factors. This observation indicates significant influence of the framework elasticity on the adsorption selectivity.