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The interaction of electromagnetic radiation in X and Ka bands with magnetic nanocomposite of disordered carbon nanotubes arrays has been investigated both experimentally and theoretically. Samples were synthesized on the quartz reactor walls by decomposition of ferrocene and xylene which provided random intercalation of iron phase nanoparticles in carbon nanotube array. The exhaustive characterization of the samples by means of the scanning electron microscopy, Raman spectroscopy, and x-ray photoemission spectroscopy was performed. It was found that the absorption of the electromagnetic wave monotonically increases with the frequency. To describe these experimental data, we extended the Bruggeman effective medium theory to a more complex case of a magnetic nanocomposite with randomly distributed spherical ferromagnetic nanoparticles in a conducting medium. The essential feature of the developed model is the consideration of the complex nature of the studied material. In particular, such important parameters as magnetic and dielectric properties of both the carbon nanotube medium and the nanoparticles, the volume concentration and the dimensions of the nanoparticles, the wave impedance of the resistive-capacitive shells of the conductive nanoparticles are explicitly taken into account in our model. Moreover, analysing the experimental results, we were able to obtain the frequency dependencies of permittivity and permeability of the studied nanocomposite.