[en] Composites of multiwalled carbon nanotubes with poly(ethylene terephthalate) (PET–MWCNT) with up to 3 vol% MWCNTs were prepared and characterized by broad-band AC conductivity and dielectric spectroscopy up to the infrared range using several techniques. A very low electrical percolation threshold of 0.07 vol% MWCNTs was revealed from the low-frequency conductivity plateau as well as from DC conductivity, whose values show the same critical power dependence on MWCNT concentration with the exponent t = 4.3. Above the plateau, the AC conductivity increases with frequency up to the THz range, where it becomes overlapped with the absorption of vibrational modes. The temperature dependence down to ∼5 K has shown semiconductor behaviour with a concentration-independent but weakly temperature-dependent small activation energy of ∼3 meV. The behaviour is compatible with the previously suggested fluctuation-induced tunnelling conductivity model through a thin (∼1 nm) polymer contact layer among the adjacent MWCNTs within percolated clusters. At higher frequencies, deviations from the simple universal conductivity behaviour are observed, indicating some distribution of energy barriers for an electron hopping mechanism. (paper)