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The authors have studied the dielectric properties of composite materials based on both thermoplastic and thermoset resins filled with nickel or copper, with various particle sizes and shapes. In addition, two types of particle distribution, random and segregated, were produced for composites filled with nickel. The main objective was to study the effect of the above factors on the dielectric properties of the composites. The concentration dependence of the dielectric parameters (i.e. the real, ∊′, and the imaginary, ∊″, parts of the complex dielectric permittivity and the dielectric loss tangent, tanδ), calculated for all the systems studied, demonstrates a critical behaviour in the percolation threshold region, with maximum values reached at a volume fraction ϕ = ϕc. The dependence of the dielectric parameters on concentration follows power-law behaviour in the ϕ < ϕc region. The critical exponent value for ∊′ is q = 0.75, in agreement with the theoretical one. The dielectric characteristics of the filled composites are more sensitive to the spatial filler distribution. For the segregated PVC-Ni system with an ordered filler distribution, the value of ϕc is much lower than for ER-Ni composites with a random filler distribution. Besides, for the segregated PVC-Ni system, the value of q is not constant, as it depends on the filler concentration. A model for the structure, which explains this behaviour, is proposed.