Composites based on ultrahigh-molecular-weight polyethylene and carbon nanotubes were obtained by mixing the components in xylene at certain temperatures. The complex conductivities and permittivities of the material samples were measured in the frequency range from 100 Hz to 1 GHz. The conditions for the synthesis of both electrically conducting and dielectric composites were established. The conductivity depends not only on the concentration of carbon nanotubes, but also on the structure of their distribution in the polymer matrix, which in turn depends on the temperature conditions for obtaining the composite.