For a polypyrrole micro-line synthesized with width down to 1.5 mu using a scanning probe microscope, the current-voltage characteristics evolve from ohmic to highly nonlinear as temperature is reduced to 50 K. We show that this nonlinearity agrees with the generic behaviour given by our full calculations for fluctuation-assisted tunnelling and thermal activation, and make a comparison with the behaviour in polypyrrole films and polyacetylene nanofibres. (C) 2004 Elsevier B.V. All rights reserved.