  Inelastic neutron scattering has been used to obtain a comprehensive
description of the absolute dynamical spin susceptibility $\chi'' (q,\omega)$
of the underdoped superconducting cuprate YBa_2 Cu_3 O_{6.5} ($T_c = 52 K$)
over a wide range of energies and temperatures ($2 meV \leq \hbar \omega \leq
120 meV$ and $5K \leq T \leq 200K$). Spin excitations of two different
symmetries (even and odd under exchange of two adjacent CuO_2 layers) are
observed which, surprisingly, are characterized by different temperature
dependences. The excitations show dispersive behavior at high energies.
