The stabilities of all possible purine/pyrimidine pairings between the isomeric nucleobases isocytosine (iso-C) and isoguanine (iso-G) and standard genomic bases are reported for two independent oligonucleotide duplexes. Additionally, results are given from ab initio calculations performed on iso-C and iso-G. The calculations are used as an aid in the interpretation of thermodynamic data obtained from duplex denaturation studies. The unnatural iso-C/iso-G pair is found to be as stable as a C/G Watson-Crick pair in both duplex systems. The next most stable unnatural pair is that formed by C/iso-G and is observed to be isoenergetic with a U/A Watson-Crick Fair. Ab initio data suggest iso-G may adopt an unprecedented imino oxo tautomer which could explain the unusual stability of the C/iso-G pair. The stability of the other possible unnatural pairs are reported and similarly interpreted in terms of ab initio and other available experimental data. Finally, the fitness is discussed of a six-component genetic system that includes iso-C, iso-G, and four standard genomic bases.