The perturbed hard-sphere-chain (PHSC) equation of state for multicomponent mixtures is presented as a generalization from the equation of state for pure fluids. The reference term, based on Chiew’s equation of state for hard-sphere chains, requires no mixing rules. Only the attractive perturbation requires van der Waals one-fluid mixing rules. Cross parameters needed in the perturbation are obtained using pure-fluid parameters and simple combining rules. The simplifying physical assumptions required to reduce the perturbation term to the Flory chi parameter are given. Specific interactions are included by adapting the model of ten Brinke and Karasz. Model calculations for binary mixtures demonstrate that the PHSC equation can predict lower critical solution temperatures, upper critical solution temperatures and closed partial-miscibility loops. Special attention is given to the effects of polymer molecular weight, pressure, differences in segment size and differences in segment interaction energy.