Carbon-13 NMR spin-lattice relaxation rates and NOEs are reported for alpha- and gamma-cyclodextrin in solution at two temperatures and four magnetic fileds, 4.7, 6.3, 9.4, and 11.8 T. In addition, transverse relaxation rates are reported at 9.4 T. The data are interpreted using the "model-free" approach of Lipari and Szabo. All the ring carbons are considered to be equivalent in the dynamic sense, while the exocyclic hydroxymethyl groups are treated separately. The multiple-field relaxation of the ring carbons can be reproduced using a truncated two-parameter model, not explicitly including the local, rapid motion correlation time. The global correlation times, on the order of a few nanoseconds, and high order parameters are obtained for the ring carbons. Several procedures for fitting the hydroxymethyl carbon data are described and compared with each other. The order parameters for these carbons are lower, and it is possible to obtain some estimates of the local motion correlation times.