Single gas and mixture permeances of CO2 and CH4 were measured as functions of pressure and temperature through three MFI zeolite membranes that have different fractions of their permeances through non-zeolite pores. The effect of pressure on CO2 permeance, which was different for each membrane, was fit by a modified surface diffusion model. The differences in the pressure behavior of the membranes are attributed to pores with viscous and Knudsen flow. Membranes with the largest permeation through non-zeolite pores have the lowest CO2/CH4 mixture selectivity. The highest CO2/CH4 mixture selectivity is 5.5 at room temperature and decreases with temperature because of a decrease in competitive adsorption. Although increasing pressure at constant pressure drop increases the apparent CO2/CH4 selectivity, the ratio of the CO2 and CH4 fluxes decreases.