The statistical associating fluid theory for potentials of variable range (SAFT-VR) is used to examine the phase behaviour in the CO2 + n-alkane homologous series. A unique set of transferable parameters for the unlike interactions are used which allow the prediction of the phase behaviour of different members of the series with little experimental data. A change in phase behaviour from type 11 in the van Konynenburg scheme (continuous gas-liquid critical line and liquid-liquid immiscibility at low temperatures) for CO2 + n-dodecane, to type IV (discontinuous gas-liquid critical line and liquid-liquid immiscibility) for CO2 + n-tridecane, and to type III (continuous transition from gas-liquid to liquid-liquid critical behaviour) for CO2 + n-tetradecane is observed in agreement with experimental data.