We propose a new theory for relating the dielectric constant to the internal structure of association fluids containing any number of associating components, the molecules of which may possess any number of electron-rich and electron-deficient sites. The theory combines concepts proposed earlier by Kirkwood (1939) for describing dielectric behavior with more recent theoretical advances made in the area of associating fluids. The derived expressions account for correlations between all pairs of dipoles located within transient associated clusters of all possible sizes, molecular sequences, and shapes, the only exception being closed-ring structures. They reduce to known forms derived earlier using other methods for relatively simple systems, such as water, alcohols, and aqueous mixtures of alcohols and ketones. An application of the theory to the DMSO-water mixture suggests two modes of association between DMSO and water molecules (in addition to that between water molecules): (i) the oxygen atom of DMSO molecules associating with the protons of water molecules, as proposed by several workers in the recent past, and (ii) the oxygen atom of water molecules associating with the sulfur atom of DMSO molecules, as proposed originally by Tomilla and Murto (1963).