The design of sour-gas treating processes with alkanolamine solvents requires knowledge of the vapour-liquid equilibrium (VLE) of the aqueous acid gas-alkanolamine systems. Representation of the experimental data with a thermodynamically rigorous model is required, so that one can systematically correlate and predict the VLEs of these systems. The modified Clegg-Pitzer equations have been used to correlate and predict the VLE Of CO2 in the aqueous N-methyldiethanolamine (MDEA) and 2-amino-2-methyl-1-propanol (AMP) systems. Differential evolution (DE), an evolutionary computational technique, has been used for parameter estimation of the developed VILE model in an effort to predict the VLE of CO2 in aqueous MDEA and AMP solutions with a comparable accuracy to that by using the non-traditional simulated annealing (SA) and deterministic technique like Levenberg-Marquardt (LM), if not better. In this work, the DE/rand-best/1/bin strategy has been used for finding near global minimum solutions to the multivariable optimization problem as a part of the numerical solution of the developed model.