Atomistic simulations are used to study the ionic liquid (IL) 1-n-hexyl-3-methylimidazolium bis(trifluoromethylsulfonypl)amide ([hmim][Tf2N]) confined into (20,20) and (9,9) carbon nanotubes (CNTs) and the effect of confinement upon gas sorption. The cations and the anions exhibit highly ordered structures in the CNT. There are more cations adsorbed close to the (20,20) tube wall while more anions adsorb in the tube center at high IL loadings. The IL molecules in the CNT exhibit self-diffusivity coefficients about 1-2 orders of magnitude larger than the corresponding bulk IL molecules. Sorption of CO2 and H-2 gases in the composite material consisting of CNT and IL indicates that H-2 molecules diffuse about 1.5 times faster than the CO2. In contrast, H-2 diffuses about 10 times faster than CO2 in both the CNT and in bulk IL. The CNT exhibits the largest amount of sorption for both CO2 and H-2, followed by the composite material, and the IL exhibits the least gas sorption. When the temperature is increased, the amount of sorbed CO2 decreases in all three types of systems (IL, CNT, and the composite material) while the H-2 sorption increases in [hmim][Tf2N], decreases in the CNT, and does not change significantly in the composite material. The composite material exhibits higher sorption selectivity for CO2/H-2 than both the IL and the CNT. It is very interesting to note that the IL molecules can be dissolved in the CO2 molecules under confinement due to a favorable negative transferring energy. However, in the absence of confinement the IL molecules will not dissolve in the CO2 due to a very large unfavorable positive transferring energy.