In this paper we present a statistical model to describe the dielectric behavior of binary solutions. The formal development is based on the introduction of a few dynamical parameters describing the interactions occurring in the solution; these parameters enter in the rate equations for the dynamics of mixing. These equations, after suitable linearization, are used as the starting point to obtain the dipole correlation functions necessary to study the dielectric relaxation processes. The model is able to indicate the conditions which a mixture composed of two liquids with very different relaxation times must fulfill to produce a single relaxation time, as often experimentally observed. Some significant results reported in the literature are analyzed and explained and new experimental data are reported in order to test specific features of the model. All tests carried out so far on binary solutions give a successful reproduction of experimental results.