When used in nucleic acid duplexes, locked nucleic acid (LNA) and 2'-O-methyl RNA residues enhance the duplex stabilities, and this makes it possible to create much better RNA aptamers to target specific molecules in cells. Thus, LNA and 2'-O-methyl RNA residues are finding increasingly widespread use in RNA-based therapeutics. Herein, we utilize molecular dynamics (MD) simulations and UV melting experiments to investigate the structural and thermodynamic properties of 13 nucleic acid duplexes, including full DNA, RNA, LNA, and 2'-O-methyl RNA duplexes as well as hybrid systems such as LNA:RNA, 2'-O-methyl RNA:RNA, LNA/2'-O-methyl RNA:RNA, and RNA/2'-O-methyl RNA:RNA duplexes. The MD simulations are based on a version of the Amber force field revised specifically for RNA and LNA residues. Our results indicate that LNA and 2'-O-methyl RNA residues have two different hybridization mechanisms when included in hybrid duplexes with RNA wherein the former underwinds while the latter overwinds the duplexes. These computational predictions are supported by X-ray structures of LNA and 2'-O-methyl RNA duplexes that were recently presented by different groups, and there is also good agreement with the measured thermal stabilities of the duplexes. We find out that the underwinding phenomenon seen in LNA and LNA:RNA hybrid duplexes happens due to expansion of the major groove widths (Mgw) of the duplexes that is associated with decrease in the slide and twist values in base-pair steps. In contrast, 2'-O-methyl RNA residues in RNA duplexes slightly overwind the duplexes while the backbone is forced to stay in C3'-endo. Moreover, base-pair stacking in the LNA and LNA:RNA hybrid systems is gradually reduced with the inclusion of LNA residues in the duplexes while no such effect is seen in the 2'-O-methyl RNA systems. Our results show how competition between base stacking and structural rigidity in these RNA hybrid systems influences structures and stabilities. Even though both LNA and 2'-O-methyl RNA residues have C3'-endo sugar puckering, structurally LNA residues have a frozen sugar backbone which provides entropic enhancement of stabilities while the 2'-O-methyl RNA residues are more flexible and maintain base stacking that is almost untouched compared to RNA. Thus, enhancement of the structural stabilities of RNA duplexes by 2'-O-methyl RNA modifications is smaller than for the corresponding LNA modifications. Indeed, our experimental measurements show that on average each 2'-O-methyl RNA and LNA substitution in a RNA duplex enhances duplex stability by 0.2 and 1.4 kcal/mol, respectively. Our computational binding free energy predictions are qualitatively in line with these results. The only exception is for the full 2'-O-methyl RNA duplex, which is overstabilized, implying that further force field revisions are needed. Collectively, the results presented in this paper explain the atomistic details of the structural and thermodynamic roles of LNA and 2'-O-methyl RNA residues in RNA hybrid duplexes, shedding light on the mechanism behind targeting endogenous micro RNA (miRNA) in order to regulate mRNA activity and inhibit gene expression in the cell.