A systematic DFT conformational studies of four building blocks of TNA with cytosine attached to the C1′ atom of the α-L-threofuranose moiety are presented. Structures bearing 2′-OR and 3′-OR substituents, where R represents H, CH3 and phosphate groups, were used in the studies using a B3LYP functional in the gas phase. The χ angle (C2-N1-C1′-O4′), the ν0-ν4 endocyclic torsion angles and the exocyclic torsion angles ε (X-O2′-C2′-C1′) and γ (X-O3′-C3′-C2′) geometry parameter variations were taken into consideration. Three energy minima, high-anti, anti and syn, were found for the rotation about the C1′-N1 bond. The high-anti orientation of the base with respect to the sugar moiety, turned out to be preferred, regardless of the substituents at the C2′ and C3′ positions. Other orientations are at least 1.65 kcal/mol higher in Gibbs free energy than the high-anti one. It has been shown that intramolecular H-bonds and the anomeric effect of phosphate groups strongly affect the conformational preferences of the studied compounds. Further, the structure of substituents attached to the sugar moiety influence the pucker of the furanoid ring. The furanoid ring in the global minima of the compound with two OH groups (TC1) in the 2′ and 3′ positions, and the compound having a 3′-phosphate group (TC2), adopt roughly the same conformation located at the southern range of the pseudorotation wheel, and thus are close to those found in the B type DNA helix. The low-energy high-anti rotamers of the geometry with the phosphate group attached to the sugar ring in the 2′ position (TC3) and the geometry with two methoxyl groups (TC4) have their furanoid rings in conformations resembling those found in A DNA and RNA helices (the northern range of the pseudorotation wheel).