Phase behavior is strongly affected by dipolar interactions in a wide range of systems including those containing ketones, aldehydes, ethers, and esters. Multiple polar sites are present in various polar copolymers as well as in polyethers and polyesters. Although theories have been developed for nearly spherical polar molecules and for nonpolar chain molecules, accounting simultaneously for a single multipolar interaction and molecular shape has remained an unsolved problem of statistical-mechanics-based perturbation theory (Gray, C. G.; Gubbins, K. E. Theory of Molecular Fluids I; Clarendon Press: Oxford, U.K., 1984. Walsh, J. M.; Gang, J.; Donohue, M. D. Fluid Phase Equilib. 1991, 65, 209). Accurate accounting for the effect of multiple polar sites in nonspherical molecules has been well beyond expectation. In recent work, we solved part of this problem by showing how to accurately predict the properties of chainlike molecules with single or multiple dipolar sites (Jog, P. K.; Chapman, W. G. Mol. Phys. 1999, 97, 307-319). Although we cast this result in terms of the original SAFT equation of state (Chapman, W. G.; Gubbins, K. E.; Jackson, G. Mol. Phys. 1988, 65, 1057-1079. Chapman, W. G. Ph.D. Dissertation, Cornell University, Ithaca, NY, 1988. Chapman, W. G.; Gubbins, K. E.; Jackson, G.; Radosz, M. Ind. Eng. Chem. Res. 1990, 29, 1709-1721), the approach is applicable to other accurate chain fluid equations of state. In this paper, we (a) demonstrate the differences between our approach and previous models, (b) extend our theory to mixtures of polar fluids, and (c) compare our results with experimental data to demonstrate the predictive capabilities of the new theory.