Sorption of pure methane, carbon dioxide and their binary mixtures in two glassy polymers, poly(1-trimethylsilyl-1-propyne) (PTMSP), and the first polymer of intrinsic microporosity (PIM-1), has been studied experimentally and theoretically, at 35.0 ºC. Measurements were obtained on a newly designed pressure decay sorption apparatus for mixtures of gases, having the basic construction according to Sanders et al. , but with a more versatile procedure than that used in , which allowed to measure sorption isotherms at constant partial pressure of one component of the gas mixture. Indeed this novel method allows one to measure sorption isotherms i) at constant composition of the gaseous phase, ii) at constant fugacity of one component or iii) at constant equilibrium pressure. The first protocol, in particular, allows to mimic better the real constraints faced when dealing with a membrane separation process, where one has a gas stream of fixed composition, in which only the total pressure can be varied, by compression. The pressure decay apparatus is coupled to a gas chromatograph Varian CP-4900 Micro-GC equipped with a capillary column and with a thermal conductivity detector for analysis of the gas phase composition. In the case of PTMSP, the mixture n-C4/CH4 was initially considered, to provide a direct comparison with literature data  and validation of the method. Indeed, the sorption of n-C4/CH4mixtures showed a reasonable agreement with the existing mixed gas sorption data . On the other hand, the CO2/CH4mixed sorption data in PTMSP are completely new, and were measured in the range from 0 to 33 atm of total equilibrium pressure, and from 5 to 90 mol.% of carbon dioxide in the gaseous phase. Furthermore, the same characterization of CO2/CH4 mixed sorption was performed in PIM-1: the pressure range inspected was the same as in PTMSP, while the composition of CO2 ranged from 10 to 50 mol.%. PTMSP membrane was cast from a solution of toluene, immersed in methanol and then dried under vacuum before characterization; its density was 0.77±0.01 g/cm3. The PIM-1 membrane was prepared from a filtered ca. 2.0 wt.% chloroform solution of PIM-1 and heated in vacuum at 70 °C, then submerged in methanol and dried under vacuum at 70 °C. The density of pure PIM-1 was (1.143±0.008) g/cm3at 25°C. For both PTMSP and PIM-1, the mixed gas solubility differs significantly from the pure gas value, and, in particular, the solubility of both components is depressed by the presence of the second one, as it often happens in glassy polymers. The solubility selectivity ranges between 2 and 6 for PTMSP and between 5 and 10 for PIM-1. The methane solubility, however, is more significantly depressed by CO2 than that of CO2 is decreased by CH4, therefore the real solubility selectivity (CO2/CH4) for PTMSP and PIM-1 is higher than the ideal solubility selectivity. Such effect becomes more significant with increasing the mole fraction of CO2 in the gaseous phase and with pressure, and is more significant for PIM-1 than for PTMSP. Indeed, the real solubility selectivity becomes 3 times higher than the ideal one in PTMSP for a fraction of 70 mol.% of CO2 in the gas phase, while for PIM-1 such point is reached with a lower concentration of CO2(50 mol.%). Both results indicate the presence of a competition for available polymer matrix sites, which is not surprising due to the nature of physical sorption in glassy matrices, and possibly also of different interactions between polymer and penetrants. To investigate that behavior, the Non-Equilibrium Lattice Fluid model (NELF) was used , while the widely used Dual Mode Sorption (DMS) model was also considered as a reference tool. The NELF model, as well as the DMS, does not require additional parameters for the prediction of the mixed gas behavior, and is fully predictive provided a few pure gas sorption data in the polymer matrix. Indeed, binary interaction parameters are the same as in the pure gas case, and the swelling induced by the mixture is estimated from pure gas swelling. Remarkably, in the DMS model, only competition (depression) effects are accounted for, because the mixed gas additional term (positive) appears only in the denominator of the expression for solubility. The NELF model provided quantitative predictions of the mixed gas sorption of CO2 and CH4under pure- and mixed-gas conditions in PTMSP and in PIM-1. The solubility selectivity is also predicted, although with less accuracy, by the NELF model. The DMS model works fairly well in the case of PTMSP, but provides poorer predictions than the NELF model of the mixed gas solubility in PIM-1. Sorption of mixtures of CO2 and CH4 in PTMSP and in PIM-1 was predictable with the NELF model with an accuracy that is comparable to the experimental one, which could reduce the need for the laborious measurements of mixed gas sorption in polymers. Better insights and interpretation of the mixed gas sorption mechanism can also be obtained by using the NELF model.