We have determined the directions and magnitudes of translational and rotational mobility of the phosphate, ribose and base moities of several ribo-oligonucleotides and of the self-complementary DNA duplex, C-G-C-G-A-A-T-T-C-G-C-G, from single-crystal X-ray diffraction data. To describe nucleic acid mobility, we have used a “segmented rigid body” model in which an oligonucleotide is divided into several subgroups, the motion of each of which is constrained to translate and librate (partially rotate) as a unit. This approach reduces the number of parameters sufficiently to allow determination of the local mobility from available experimental data. Our results show that double-stranded DNA and double-stranded RNA have similar local mobilities. Some of the types of mobility that we observed for double helices are as follows. 1. (1) Propeller twisting between paired bases and rolling of the base-pairs as a unit. 2. (2) Buckling of the base-pairs. 3. (3) Sliding of the bases in the plane of the base-pairs. 4. (4) Coupled rotation of the sugar and base as a nucleoside unit. 5. (5) Coupled translation of paired bases. 6. (6) Fluctuation of the groove sizes or bending of the helices. 7. (7) Unwinding/winding motion at the ends of helices. We have also noted a dependence of mobility in double helices on base type as well as location of the residue relative to the helical ends. These observed local mobilities can help us understand conformational changes during such processes as intercalation, melting, supercoiling, interconversion of helical forms, packaging of DNA in nucleosomes, and interaction of nucleic acids with proteins and other ligands. Somewhat different mobilities are observed for RNA fragments that are not involved in Watson-Crick base-pairing. For example, the major single-stranded base libration axis corresponds to a simple rotation around the glycosyl bond. Also, there does not appear to be a coupling of the librational mobility of the ribose and base like that observed for the double-stranded oligonucleotides. Differences in mobility and flexibility between single and double-stranded nucleic acids may be important for recognition and binding of nucleic acids by proteins. Thus, use of a segmented rigid body model has allowed us to develop a detailed picture of the local dynamics of nucleic acids based strictly on experimental data.