SAFT-VR Mie is extended to quadrupolar molecules and their mixtures by incorporating an explicit Helmholtz contribution for quadrupole-quadrupole interactions. Two quadrupolar terms are considered: the quadrupolar theory of Larsen and coworkers, and that of Gross, yielding VRM-L and VRM-G, respectively. Each model requires an additional parameter for quadrupolar molecules. The two quadrupolar models are evaluated by means of their ability to model the following binary systems: CO2 or benzene with n-alkanes or 1-alkanols and binary mixtures of quadrupolar molecules. VRM-L and VRM-G offer significant improvements over nonpolar SAFT-VR Mie in describing the VLE of the CO2 + n-alkane systems, while only the benzene + n-hexane system requires the additional quadrupolar term for accurate description. Cross-association in CO2 + 1-alkanol systems is accounted for by fine-tuning the association parameters of CO2, resulting in an improved description of these systems using VRM-G. Less promising results are obtained with VRM-L. VRM-L and VRM-G can describe benzene + 1-alkanol systems without cross-association. The quadrupolar models can qualitatively represent the VLLE of CO2 + n-alkane and CO2 + 1-alkanol systems. Good predictions of the CO2 + benzene system are obtained with both VRM-L and VRM-G when only CO2 is modeled as quadrupolar.