Bulge insertions of conjugated intercalators into the DNA triplex structure are found to give a dramatic contribution to the triplex stability. On the other hand insertions of conjugated intercalators are found to diminish quadruplex structures and in this way breaking down the self association of G-rich oligonucleotides under physiologically potassium ion conditions. A large number of intercalators are described here and they all result in dramatic increases of thermal stability of the corresponding triplexes. Another interesting aspect of conjugated intercalators is their use for assembling alternate strand triplexes. Targeting of neighbouring purine sequences on each their strand in the duplex DNA is a challenge for the 5'- 5' connectivity of the TFOs because of a large distance between the 5'-ends. The intercalator approach offers a linkage with the proper combination of flexibility and rigidity to produce alternate strand triplexes with higher stability than a similar wild type triplex of the same total length.