The current-voltage (I-V) characteristics of individual nanofibres of doped polyacetylene show a dramatic change from very strong nonlinearities for lightly-doped samples at low temperatures, to nearly ohmic behaviour for higher temperatures and doping levels. At low temperatures (below 10-30 K), the I V characteristics are independent of temperature and follow the expression for Zener-type tunnelling, as predicted for field-induced tunnelling of the conjugated bond system. At higher temperatures, the I-V characteristics deviate from Zener-type behaviour and the current increases with temperature as thermally-assisted conduction mechanisms become important. The I-V characteristics for the most conductive sample are consistent with our calculations of fluctuation-induced tunnelling. (C) 2002 Elsevier Science B.V. All rights reserved.