A membrane gas CO2 capture setup, based on the concept of single module absorption and single cycle coupled absorption/desorption, was developed in this work. Ionic liquids (ILs) 1-ethyl-3-methylimidazolium methylsulfate ([emim][MS]) and 1-ethyl-3-methylimidazolium dicyanamide ([emim][DCA]) were used as absorbents. The CO2 absorption rate decreased initially and reached to a nearly constant value achieving pseudo steady state. Coupled absorption/desorption revealed very high performance by retaining 82% and 66% absorption efficiency, for [emim][MS] and [emim][DCA], respectively, even after 70 minutes of operation. Mass transfer coefficients of the coupled absorption/desorption at pseudo steady state were 9 and 5 folds higher than single module absorption, for [emim][MS] and [emim][DCA], respectively. Parametric analysis for the membrane absorber outlet concentration and optimization of the parameters to achieve zero concentration at the membrane stripper outlet were studied in simulations. As a conclusion, coupled absorption/desorption in combination with ILs, can be considered very suitable for continuous post-combustion carbon capture.