We have measured the temperature and magnetic field dependence of the Cu nuclear spinlattice relaxation rate W and its anisotropy r at plain Cu(2) sites in normal and superconductingYBagCu40s. Below T, we observed that an applied magnetic field B II c enhances W = W"whereas B J c suppresses R' = W g. Such a behavior seems to rule out the spin diffusion to the fluxoid cores and the fluxoid motion as being responsible for the effect. It indicates more an unexpected field-related breaking of the spin-rotation invariance in the superconducting state. The anisotropy r defined as the ratio W, b/W, is almost field and temperature independent in the normal state but develops a nonmonotonic temperature dependence below T, with a flat minimum at 45 K in B = 5.17 T and a much more pronounced minimum at 55 K in B = 0.58 T. A qualitatively similar behavior of r has been reported previously for YBa2Cu30p. Comparing r in both compounds, we note one essential difference at low B. Namely, the slope dr/dT just below T, is large for YBa2Cu30& but almost zero for YBa2Cu408.Nuclear magnetic resonance and neutron-scattering experiments have shown that spin fiuctuations in hightemperature superconductors have strong antiferromagnetic (AFM) correlations, which persist into the superconducting state. The study of the temperature and field dependence of the NMR spin-lattice relaxation rate W, where o; = a, b, or c specifies the orientation of the static applied field B, and its anisotropy r = W b/W, at the Cu plane site [(Cu(2)] may help to understand how these AFM correlations are affected by superconductivity.Recently, it was reported ' that in YBa&Cus0& (abbreviated 1-2-3) measurements of W and r in the superconducting state appear to require a modification of theories such as that by Millis, Monien and Piness but agree qualitatively with the orbital-d-wave fits by Bulut and Scalapino4s and Lu. s In addition, Martindale et aL2 found that in the superconducting state W"and to a lesser degree W b, become enhanced in a magnetic field, with the enhancement growing at lower temperature. A temperature-dependent anisotropy below T, in 1-2-3 has also been studied in low magnetic field by Takigawa, Smith, and Hulst. "We have reported previouslys similar investigations of W~anisotropy and its field dependence for Cu(2) in the stoichiometric double-chain compound YBazCu40s (1-2-4), which has the same Cu-0 plane structure as 1-2-3 but lower charge-carrier concentration. In particular, the Cu(2) rate W" field independent in the normal state, shows a field-dependent enhancement in the superconducting state that already begins 13 K above T, in a 5.17 T field. Consequently the anisotropy r that is temperature and field independent above T, + 13 K (r = 3. 3) starts to diminish below this temperature. Down to 80 K the reduction of r is hardly noticeable. However, below that temperature r drops very rapidly to a value of 2.2 and after passing a flat minimum at 45 K it increases again at lower temperature.Since in the superconducting state the change of r...