  We investigate nuclear spin-lattice relaxation data in the normal state of
optimally doped YBaCuO_7 by analyzing the contributions to the relaxation rate
of the copper, planar oxygen and yttrium along the directions perpendicular to
the applied field. In this new picture there is no contrasting temperature
dependence of the copper and oxygen relaxation. We use the model of fluctuating
fields to express the rates in terms of hyperfine interaction energies and an
effective correlation time tau_eff characterizing the dynamics of the spin
fluid. The former contain the effects of the antiferromagnetic static spin
correlations, which cause the hyperfine field constants to be added coherently
at low temperature and incoherently at high temperature. The degree of
coherency is therefore controlled by the spin-spin correlations. The model is
used to determine the temperature-dependent correlation lengths. The
temperature-dependent effective correlation time is found to be made up of a
linear and a constant contribution that can be related to scattering and spin
fluctuations of localized moments respectively. The extrapolation of our
calculation at higher temperature fits the data also very well at those
temperatures. The underdoped compounds YBaCuO_6.63 and YBaCuO_8 are studied in
the limit of the data available with some success by modifying the effective
correlation time with a gap parameter. The copper data of the LaSrCuO series
are then discussed in terms of the interplay between the two contributions to
tau_eff.
