We study the electronic transport properties of quasi-one-dimensional
winding chains with random loops by an exact self-consistent recursion
method. We obtain groups of states with very long localization length
s which can lead to high values of the conductance. The energy distrib
ution of these states causes unusual transport properties, similar to
the behavior found near a metal-insulator transition. Our results demo
nstrate the importance of the winding structures for explaining the pr
operties of highly conducting polymers since the obtained temperature
and magnetic-field dependences of the conductance in the presence of l
ow loop density show good agreement with recent experimental results.