The estimation of the solubility of fluid mixtures in polymeric phases is an essential prerequisite for membrane separations and in the design of several devices, such as chemical sensors: the presence of swelling and strongly interacting components in the fluid mixture can often cause rather large deviations from the pure component sorption behavior. For rubbery polymers, the usual equilibrium tools such as the multicomponent versions of the equation of state (EoS) models can be adopted, while for the case of glassy polymers, which are not at equilibrium, such an approach cannot be followed. The general model called nonequilibrium thermodynamics of glassy polymers (NET-GP) has proved to be a successful tool for predicting the solubility of pure gases, vapors and liquids in glassy polymers, and it is here applied to the prediction of multicomponent fluid solubility. In particular, three gas-gas-polymer systems, which show significant deviations from the ideal behavior, are examined at room temperature and various pressures: CH4/CO2 in poly(2,6-dimethyl-1,4-phenylene oxide) (PPO), C2H4/CO2, and N2O/CO2 in poly(methyl methacrylate) (PMMA). The maximum deviation between experimental data and the model predictions is equal to 10%, using as input only the pure component parameters and the binary parameters evaluated from pure gas sorption data. The model thus proves to be a reliable tool to estimate the mixed gas solubility in glassy polymers, in the common case in which such data are not experimentally available for the system of interest.