Using the statistical association fluid theory-hard spheres (SAFT-HS) equation of state for chain molecules and its recent extension to ring molecules, phase diagrams for model mixtures of types (m(1)-sphere chain + m(2)-sphere chain) and (m(1)-sphere chain + m(2)-sphere ring) have been calculated. The influence of chain length, relative sphere size, relative mean-field attraction, and reduced temperature has been investigated. In a first ever application of the SAFT-HS model to cyclic molecules, the theoretical predictions have been compared with experimental data for a variety of systems involving both chain and cyclic molecules. The experimental results confirm the predictions of the theory for the effect of a cyclic molecular structure on the phase behavior of binary mixtures.