Each component of a gas mixture affects the permeation of the other gases. This mutual influence was systematically investigated for binary gas mixtures that included CO2, N-2, CH4, H-2, and CO permeating through thermally rearranged poly(benzoxazole-co-imide) (TR-PBOI) membranes. The mixed gas permeation was measured at 35 degrees C at up to 5 bar of feed pressure. Sorption isotherms of binary mixtures were calculated using the Grand Canonical Monte Carlo approach for quantifying the sorption contribution to the permeation. The diffusivity contribution was estimated by using the permeability value. How and how much CO2 (the most soluble gas) and H-2 (the fastest diffusing gas among the gas species tested) affect each other's permeation as well as the permeation of the other gases were specifically addressed, including a discussion based on sorption and diffusion contributions. The permeance of CO2 and H-2 remained unchanged, whereas the permeance of the other gases was reduced by the presence of CO2 or increased by the presence of H-2.