We present a new set of nanostructured composites which can exhibit a phenomenon known as surface plasmon resonance in a broad frequency range from the deep infrared to the terahertz region. The structures are composites of two different kinds of non-overlapping spheres. These spheres are made from a high refractive index nonplasmonic material and a Drude-like plasmonic material. Our results are explained in the context of the extended Maxwell–Garnett theory. The effective permittivity and refractive index of zinc sulfide/Ge and zinc oxide/Ge composites have been calculated over terahertz frequencies.