In this work the electrical response of a mixture composed of dielectrically nonlinear ellipsoids dispersed in a linear matrix is modeled. The inclusions may be randomly oriented. The aim is both to set up a methodology apt to deal with this kind of system and to use it to study the effect of marked nonsphericity of inclusions on the global behavior of a mixture. The results are quite interesting from both these points of view. The method here developed extends the Maxwell-Garnett theory [A Treatise on Electricity and Magnetism (Clarendon, Oxford, 1881)], which deals with dielectrically linear inclusions, and it allows, inter alia, to obtain a closed-form expression for the hypersusceptibility ratio of the mixture to the dispersed inclusions. These latter can range from cylinders to spheres, already present in the literature, to âpenny-shapedâ particles. The theoretical framework is based on the assumption that the dispersion is very dilute. We were able to show that in a specific case, when oblate particles such as elliptic lamellae are dispersed in a matrix having dielectric constant lower than the linear term of inclusion permittivity, a remarkable nonlinear effect occurs. This theory finds application in fields such as nonlinear optics and, more broadly, in many branches of material science.