A literature survey was performed to evaluate the state-of-the-art membrane systems for CO₂/CH₄ separation which is critical in the natural gas industry. The systems that were reviewed included zeolite, carbon, polymeric, mixed matrix, amorphous silica, and supported ionic liquid membranes. Supported ionic liquid CO₂/CH₄ selective membranes were synthesized in our laboratory by applying room temperature ionic liquids (RTILs) to porous inorganic α-alumina supports. The supported ionic liquid membranes (SILMs) displayed CO₂ permeance of 1x10⁻⁹ to 3x10⁻⁸ mol m⁻² s⁻¹ Pa⁻¹ and CO₂/CH₄ selectivity of up to 50 which is comparable with the current polymeric separation systems. It is concluded that, although the RTIL membranes showed good CO₂/CH₄ selectivity, the CO₂ permeance was too low for industrial applications. A new type of SILM was prepared by dissolving 1-aminopyridinium iodide which contained amine functionality in other ionic liquids which improved the CO₂ permeance and selectivity of these membranes. The H₂ gas separation is an important process because it has many industrial applications in petroleum processing and chemical synthesis. Amorphous silica membranes for H₂ separation were prepared on hollow fiber (HF) inorganic supports using chemical vapor deposition (CVD) of tetraethyl orthosilicate (TEOS). These membranes exhibited good H₂ permeance on the order of 10⁻⁷ mol m⁻² s⁻¹ Pa⁻¹ together with H₂/CO₂ selectivity of over 100. The separation was achieved using a new hybrid intermediate layer that was developed by depositing a mesoporous silica layer on top of γ-alumina. / Master of Science