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A theoretical investigation of the terahertz properties of composite materials containing carbon nanotubes (CNTs) was carried out. An integral equation to determine the electromagnetic response of an isolated CNT of finite length was formulated using effective boundary conditions on the surface of the CNT. Two different homogenization approaches were adopted for different frequency ranges. The obtained numerical results are in good agreement with experimental data for a wide ranges of frequencies and temperatures. Our approach yields a partial physical interpretation of an experimentally observed peak in the effective conductivity of the composite material.