Broadline ('1)H and high resolution ('13)C solid state nuclear magnetic resonance investigations of the dynamics of (alpha) and (beta) cyclodextrins, dextran, and their deuterated analogues in powders are reported. Qualitative spectral density functions are obtained for the kHz range motions from T(,1(rho)), T(,1d), and T(,2) measurements. Faster motions were sampled with frequency dependence studies of T(,1). From the relative proportions of the relaxation decays and lineshapes, it was possible to correlate these relaxation parameters with different segments of the molecules. Temperature dependence studies of T(,1), T(,1d) and the lineshape yielded some energies of activation and a correlation time for relaxation processes in (alpha) cyclodextrin. The results of these and other spin dynamics experiments are discussed in light of x-ray crystal and molecular structures;A new approach is proposed for the analysis of chemical shift data of proteins obtained from two-dimensional NMR experiments. Rather than studying the individual shifts of different atoms in a protein, statistical methods are applied to analyze the collection of chemical shifts of the whole molecule. Distribution functions for the spacing between nearest-neighbor energy levels are presented in the context of random matrix theory. The distribution of energy levels as a function of energy is characterized by a power law dependence. Randomness in a sequence of eigenvalues is also discussed. These methods reduce and classify the large data base of chemical shifts in proteins, which simplify the information content of their spectra.