In this paper we have systematically studied how the replacement of a benzene ring by a heterocyclic compound in oligo(phenyleneethynylene) (OPE) derivatives affects the conductance of a molecular wire using the scanning tunneling microscope-based break junction technique. We describe for the first time that OPE derivatives with a central pyrimidine ring can efficiently link to the gold electrode by two pathways presenting two different conductance G values. We have demonstrated that this effect is associated with the presence of two efficient conductive pathways of different length: the conventional end-to-end configuration, and another with the one of the electrodes linked directly to the central ring. This represents one of the few examples in which two defined conductive states can be set up in a single molecule without the aid of an external stimulus. Moreover, we have observed that the conductance through the full length of the heterocycle-based OPEs is basically unaffected by the presence of the heterocycle. All these results and the simplicity of the proposed molecules push forward the development of compounds with multiple conductance pathways, which would be a breakthrough in the field of molecular electronics.