Computing bubble-points of multicomponent mixtures using Monte Carlo simulations is a non-trivial task. A new method is used to compute gas compositions from a known temperature, bubble-point pressure, and liquid composition. Monte Carlo simulations are used to calculate the bubble-points of carbon dioxide (CO2) and methane (CH4) mixtures in the ionic liquids (ILs) 1-n-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide [bmim][Tf2N] and 1-ethyl-3-methylimidazolium diethylphosphate [emim][ depi. The Continuous Fractional Component Monte Carlo (CFCMC) method in the osmotic ensemble has been used to compute the solubility of CO2/CH4 gas mixtures at different temperatures (T), pressures (P), and gas compositions (y(i)). The effect of T, P, and y(i) on the real CO2/CH4 selectivity (i.e., the selectivity of CO2 in the presence of CH4) is investigated. The real selectivity will differ from the ideal selectivity, which is defined as the ratio of the Henry's constants, if the solubility of CO2 is influenced by the presence of CH4. The computed real selectivities are compared with the experimentally obtained real and ideal selectivities. The real CO2/CH4 selectivity decreases with increasing temperature and pressure, while the gas phase composition has a minor effect. The real selectivity is approximately identical to the ideal selectivity for relatively low pressures and low solute concentrations in the liquid phase. The real selectivity deviates from the ideal selectivity as the solute concentration in the liquid phase increases. (C) 2015 Elsevier B.V. All rights reserved.