DC and AC electrical conductivity of bionanocomposites based on the immiscible polymer blend poly(epsilon-caprolactone)/polylactide (PCL/PLA, w/w 70/30), loaded with multiwall carbon nanotubes (CNT), were studied in a wide frequency range, 10(-3) <= f <= 10(7) Hz from 143 to 313 K. The nanofiller concentration ranged from 0 to 4 wt % and it was shown to be selectively located in the PCL phase. The PCL crystallinity degree was not affected by the presence of CNT. The variation of the DC conductivity allowed the determination of the percolation threshold, p(c) = 0.98 wt %, and the critical exponent t = 2.2 of the scaling law. The linear dependence of log (sigma(DC)) versus p(-1/3) showed the existence of tunneling conduction among CNT not yet in physical contact. The temperature independent results indicated a conventional tunnel effect. The AC conductivity of the nanocomposites followed the predictions of the universal dynamic response and the s exponents were determined at low concentrations. Master curves are presented showing the length and temperature time superpositions.