  Unpolarized inelastic neutron scattering is used to study the temperature and
wave vector dependence of the dynamical magnetic susceptibility,
$\chi''(q,\omega)$, of a well characterized single crystal $YBa_2Cu_3O_{6.6}$
($T_c=62.7$ K). We find that a pseudogap opens in the spin fluctuation spectrum
at temperatures well above $T_c$. We speculate that the appearance of the low
frequency incommensurate fluctuations is associated with the opening of the
pseudogap. To within the error of the measurements, a gap in the spin
fluctuation spectrum is found in the superconducting state.
