  We present results of neutron scattering experiments on YBa2Cu3O6.95
(Tc=93K). Our results indicate that magnetic collective modes due to correlated
local moments are present both above and below Tc in optimally doped YBCO. The
magnon-like modes are robust and not overdamped by itinerant particle-hole
excitations, which may point at a substantial static or slowly fluctuating
charge inhomogeneity. We compare the experimental results to predictions of the
Fermi liquid (FL) theory in the Random Phase Approximation (RPA).
