Conducting polymers are a topic of great interest in the field of molecular electronics as well as for sensor applications. In this paper, we present a model for the evaluation of the d.c. conductance of a layer of conductive polymers, whose thickness is negligible if compared with the lateral extension. In our model all the monomers constituting a chain are represented by resistors with a fixed value of conductance and are disposed in a square network. The nodes of the network are structured in such a way that each monomer converging to the node under consideration can be connected to all the other three through resistors of different value:, whose alternated occurrence is ruled by a probabilistic law. The global conductance of such a network is studied while the values of the probabilities referred to the above-said occurrences are varied. Finally, the treatment of this network according to the traditional theory of random networks is considered.