  We analyze single-particle electronic and two-particle magnetic properties of
the Hubbard model in the underdoped and optimally-doped regime of \YBCO by
means of a modified version of the fluctuation-exchange approximation, which
only includes particle-hole fluctuations. Comparison of our results with
Quantum-Monte Carlo (QMC) calculations at relatively high temperatures ($T\sim
1000 K$) suggests to introduce a temperature renormalization in order to
improve the agreement between the two methods at intermediate and large values
of the interaction $U$.
  We evaluate the temperature dependence of the spin-lattice relaxation time
$T_1$ and of the spin-echo decay time $T_{2G}$ and compare it with the results
of NMR measurements on an underdoped and an optimally doped \YBCO sample. For
$U/t=4.5$ it is possible to consistently adjust the parameters of the Hubbard
model in order to have a good {\it semi-quantitative} description of this
temperature dependence for temperatures larger than the spin gap as obtained
from NMR measurements. We also discuss the case $U/t\sim 8$, which is more
appropriate to describe magnetic and single-particle properties close to
half-filling. However, for this larger value of $U/t$ the agreement with QMC as
well as with experiments at finite doping is less satisfactory.
