Ceramic composites [xNi 0:15 Cu 0:30 Zn 0:55 Fe 2 O 4 -(1 À x)BaTiO 3 ] were successfully prepared by a direct solid-state reaction of raw materials (BaCO 3 , CuO, -Fe 2 O 3 , NiO, TiO 2 , and ZnO). The composites are so homogeneous that the ferrite and BaTiO 3 grains do not react with each other. The x-dependent permeability and permittivity are found to obey Maxwell-Garnett effective medium theory, which suggests that the composites consist of ferrite particles with barium titanate medium. This model, however, starts to deviate from the experimental data at x ¼ 0:75, and the roles of medium and inclusions seem to be exchanged. It can be qualitatively explained by the fact that geometrical close-packing of spheres is limited up to about 74 vol % (Kepler conjecture).