The Peng-Robinson (PR) and cubic-plus-association (CPA) equations of state are used to predict the phase behavior and solubility of CO2 and normal alkanes from C-1 to nC(10) in several bitumens. Both of the equations of state are investigated over wide ranges of temperature and pressure. The results show that the PR-EOS describes mixure of bitumens with CO2 and alkanes when there is no second liquid phase or when the asphaltene content in the second liquid phase is not high. The CPA-EOS describes the phase behavior of mixtures of bitumens and CO2 and alkanes in liquid-liquid states even when the asphaltene content of one of the phases is high. High asphaltene content results in significant association and cross-association where the CPA-EOS is a natural choice. In this work the only adjustable parameter in the CPA-EOS is the cross-association energy parameter, and we show that the solubility of CO2 and alkanes in bitumens is usually not sensitive to this parameter. However, in two-phase liquid-liquid and three-phase liquid-liquid-vapor states with one phase having a high concentration of asphaltenes, the results become sensitive to the cross-association energy parameter.