Scanning tunneling microscope break junction measurements are used to examine how the molecular conductance of nucleic acids depends on the composition of their backbone and the linker group to the electrodes. Molecular conductances of 10 base pair long homoduplexes of DNA, aeg-PNA, γ-PNA, and a heteroduplex of DNA/aeg-PNA with identical nucleobase sequence were measured. The molecular conductance was found to vary by 12 to 13 times with the change in backbone. Computational studies show that the molecular conductance differences between nucleic acids of different backbones correlate with differences in backbone structural flexibility. The molecular conductance was also measured for duplexes connected to the electrode through two different linkers, one directly to the backbone and one directly to the nucleobase stack. While the linker causes an order-of-magnitude increase in the overall conductance for a particular duplex, the differences in the electrical conductance with backbone composition are preserved. The highest molecular conductance value, 0.06G0, was measured for aeg-PNA duplexes with a base stack linker. These findings reveal an important new strategy for creating longer and more complex electroactive, nucleic acid assemblies.