In this work, 72 new experimental solubility data points for H₂S and CO₂ mixtures in aqueous N-methyldiethanol amine (MDEA) solutions at different methane partial pressures (up to 69 bara) are presented. They are correlated using an electrolyte equation of state (E-EOS) thermodynamic model. This model has already been used to estimate the CO₂ solubility in aqueous MDEA (Huttenhuis et al. Fluid Phase Equilib. 2008, 264, 99−112) and the H₂S solubility in aqueous MDEA (Huttenhuis et al. Int. J. Oil, Gas Coal Technol. 2008, 1, 399−424). Here, the model is further extended to predict the behavior of CO₂ and H₂S when they are present simultaneously in aqueous MDEA. The application of an equation of state is a new development for this type of system, i.e., of acid-gas−amine systems. The molecular interactions are described by Schwarzentruber et al.’s modification of the Redlich−Kwong−Soave equation of state, with terms added to account for ionic interactions in the liquid phase. The model is used to describe acid-gas solubility data for the CO₂−H₂S−MDEA−H₂O system reported in the open literature and experimental data reported here for the CO₂−H₂S−MDEA−H₂O−CH₄ system.