NMR transverse relaxation (TR) measurements of O-17(2,3) in YBa2Cu3((O
1-cOc)-O-16-O-17)(7) are presented. A Gaussian-like relaxation is foun
d. The origin of this relaxation is investigated by varying c, the tem
perature, the external field, and by comparing it with the O-17(4) sit
e. Our results are consistent with a model in which this relaxation is
caused by the dynamical fluctuation of copper nuclei, including both
spin-lattice and flip-flop processes. With this model; we can also exp
lain the TR of Y-89 and Cu-63(1). We use our results to reanalyze prev
ious NMR Cu-63(2) TR data and find the dynamical exponent z = 1.