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We performed 205 Tl NMR on aligned single crystals of the 105-K superconductor Tl 2 Ba 2 CaCu 2 O 8 in a field of 4.7 T as a function of angle between the field direction and the c axis. Irreversibility temperatures T irr were determined by comparing the NMR linewidths after field cooling and zero-field cooling. The 205 Tl nuclear transverse relaxation rate T 2 Ϫ1 shows a well-developed peak caused by vortex motion below T irr . The peak shifts to higher temperatures with increasing . The data are analyzed analytically and by computer simulation and the obtained parameters of local vortex motion are discussed.A characteristic feature of the phase diagram of high-T c superconductors as a function of magnetic-field B 0 and temperature T is the presence of an extensive vortex fluid phase, that starts just below T c , and a vortex glass phase at low temperatures. 1,2 The transition from vortex fluid to vortex glass state has been studied intensively mainly by macroscopic methods ͑linear and nonlinear conductivity and magnetic measurements͒. Scaling theories for the critical slowing down of the vortex motion at this transition have been developed and applied to the results of these experiments. 1,2 Nuclear magnetic resonance ͑NMR͒ is a powerful tool to study local magnetic-field fluctuations caused by vortex motion -by the inherent short length scales, these fluctuations are not described by the renormalization theories. Various NMR properties are suited. For example, vortices give an inhomogeneous broadening of the nuclear resonance line, which effect is reduced by thermally activated vortex motion and the corresponding correlation time can be measured by NMR. 3-7 The fluctuating magnetic fields caused by vortex motion can also be studied by means of the nuclear relaxation. 7-13 The nuclear-spin-lattice relaxation T 1 is sensitive to transverse field fluctuations near the Larmor frequency 0 ϭ␥ n B 0 . Recently a peak in T 1 (T) has been observed by 199 Hg NMR in HgBa 2 CuO 4ϩ␦ (T c ϭ 96 K͒ at the irreversibility temperature, T irr . 8 The transverse relaxation or spin-echo decay time T 2 is sensitive to motions that are typically a few orders of magnitude slower than seen in T 1 , and the field fluctuations that cause the relaxation are along the B 0 direction. T 2 Ϫ1 was studied in oriented powder of YBa 2 Cu 3 O 7-␦ where the 89 Y transverse relaxation rate T 2 Ϫ1 (T) shows a peak below T c . 9 The peak was analyzed in terms of fluctuations in the vortex field gradients. In oriented powder Tl 2 Ba 2 Ca 2 Cu 3 O 10 (T c ϭ 120 K͒ by NMR on the thallium nuclei located in the TlO layers, a similar peak was observed at 35 K and explained as the crossover of time scales with and without vortex motion. 12 In this paper we present data on aligned crystals of Tl 2 Ba 2 CaCu 2 O 8 (T c ϭ 105 K͒, that give the precise location of the peak with respect to the irreversibility line and show its variation in location and height as a function of field along the c axis. The effect of vortex field fluctuations on the nuclear transve...