A study is presented of the electrical properties of a series of nanocomposites based on high density polyethylene (HDPE) as a matrix and either carbon nanofiber (CNF) or multiwall carbon nanotube (MWCNT) as a nanoadditive. The measurements of the electrical conductivity over a broad-band of frequencies (10(-2) > F/Hz > 10(9)) allow improvement of the description of the electrical properties of polymer nanocomposites based on either carbon nanofibers or carbon nanotubes. Despite the lack of a continuous conducting network between particles at low concentrations, the nanocomposites exhibit a significant dc electrical conductivity due to tunnel conduction. At low nanoadditive concentrations, the frequency dependence of the electrical conductivity is mainly caused by the influence of large polymeric gaps between conducting clusters. As nanoadditive concentration increases, the size of the finite-size cluster tends to increase and the frequency dependence of the conductivity reflects the features of anomalous diffusion in fractal structures, as expected according to percolation theory. A master curve for the electrical conductivity as a function of frequency can be constructed although, for the investigated nanocomposites, this behavior should be contemplated as a working, rather than as a universal, law.