A variety of models incorporating internal motion, which can be used to extract information from nuclear magnetic resonance relaxation studies of deoxyribonucleic acid fragments, are formulated. Illustrative analyses of some recent multinuclear relaxation data are presented. Special emphasis is placed on determining whether the information extracted is unique. It is shown that the data are consistent with several physical pictures of the internal motion. However, all the models we have considered imply the existence of large-amplitude internal motions on the nanosecond time scale.