This review describes the conformations of nucleic acids and oligonucleotides containing cyclonucleoside residues. From the studies on the oligomers of cyclonucleosides, it was demonstrated that oligonucleotides having a high anti glycosidic conformation can make up a left-handed helical system in contrast to the right-handed helical system of natural nucleic acids. Other left-handed helical structures which have been recently discovered or proposed are also reviwed. It is concluded that the glycosidic conformation in the monomer unit of nucleic acids play an important role in determining the handedness of the helical structures.