We report on several weak interactions in nucleic acids, which, collectively, can make a nonnegligible contribution to the structure and stability of these molecules. Fragments of DNA were obtained from previously determined accurate experimental geometries and their electron density distributions calculated using density functional theory (DFT). The electron densities were analyzed topologically according to the quantum theory of atoms in molecules (AIM). A web of closed-shell bonding interactions is shown to connect neighboring base pairs in base-pair duplexes and in dinuleotide steps. This bonding underlies the well-known pi-stacking interaction between adjacent nucleic acid bases and is characterized topologically for the first time. Two less widely appreciated modes of weak closed-shell interactions in nucleic acids are also described: (i) interactions between atoms in the bases and atoms belonging to the backbone (base-backbone) and (ii) interactions among atoms within the backbone itself (backbone-backbone). These interactions include hydrogen bonding, dihydrogen bonding, hydrogen-hydrogen bonding, and several other weak closed-shell X-Y interactions (X, Y = 0, N, C). While each individual interaction is very weak and typically accompanied by perhaps 0.5-3 kcal/mol, the sum total of these interactions is postulated to play a role in stabilizing the structure of nucleic acids. The Watson-and-Crick hydrogen bonding is also characterized in detail at the experimental geometries as a prelude to the discussion of the modes of interactions listed in the title.