Described is a systematic study of the effects of varied backbone structure on the stabilities of pyr.pur.pyr triple helices. The effects were measured using six circular 34 base oligonucleotides containing DNA (D), RNA (R) and/or 2'-O-methyl-RNA (M) residues designed to bind a complementary single-stranded purine target strand by triple helix formation. Eighteen different backbone combinations were studied at pH 5.5 and 7.0 by optical melting experiments and the results compared with the stabilities of the corresponding Watson-Crick duplexes. When the target purine strand is DNA, all circles form pH-dependent triple helical complexes which are considerably stronger than the duplexes alone. When RNA is the target, five of the nine complexes studied are of the pH-dependent triplex type and the other four complexes are not significantly stronger than the corresponding duplexes. The results are useful in the design of the highest affinity ligands for single- and double-stranded DNAs and RNAs and also point out novel ways to engender DNA- or RNA-selective binding.