  We present a study of the spin dynamics of magnetic defects induced by Li
substitution of the plane Cu in the normal state of YBa$_2$Cu$_3$O$_{6+x}$. The
fluctuations of the coupled Cu magnetic moments in the vicinity of Li are
probed by near-neighbour $^{89}$Y {\it and} $^7$Li NMR spin lattice relaxation.
The data indicates that the magnetic perturbation fluctuates as a single entity
with a correlation time $\tau$ which scales with the local static
susceptibility. This behaviour is reminiscent of the low $T$ Kondo state of
magnetic impurities in conventional metals. Surprisingly it extends well above
the ``Kondo'' temperature for the underdoped pseudogapped case.
