The current-voltage (I-V) characteristics of individual nanofibres of lightly-doped polyacetylene show very strong nonlinearities. At low temperatures the I-V characteristics are consistent with Zener-type tunnelling. and independent of temperature and magnetic field. We propose that this behaviour arises from tunnelling of a segment of the conjugated bond system in the presence of an electric field, in analogy to the soliton-pair creation mechanism proposed by Maki for conduction in charge-density-wave (CDW) materials. A comparison is made with analogous tunnelling conduction mechanisms reported in CDW and spin-density-wave systems at low temperatures. At higher temperatures the I-V characteristics deviate from Zener-type behaviour and are temperature dependent, so other conduction mechanisms are important. (C) 2002 Elsevier Science B.V. All rights reserved,