  We perform a comprehensive analysis of the dynamical magnetic susceptibility
\chi(q,\omega) in the slave-boson mean-field scheme of the bilayer t-J model.
In the d-wave pairing state, the strongest magnetic spectral weight appears at
q=Q=(pi,pi) and \omega=\omega_{Q}^{res}, and spreads into a diamond-shaped
shell around Q in q space for \omega<\omega_{Q}^{res}. This weight is due to a
collective mode, namely a particle-hole bound state, which has a downward
\omega versus q dispersion around Q. Within the high intensity shell, the
incommensurate (IC) signals at q=(pi,pi\pm 2pi\eta) and (pi\pm 2pi\eta,pi) tend
to be stronger than the diagonal incommensurate (DIC) signals at q=(pi\pm
2pi\eta',pi\pm 2pi\eta'), especially for a large hole density \delta. For
\omega \ll \omega_{Q}^{res} the IC signals completely disappear and the weight
remains only around the DIC positions. For \omega > \omega_{Q}^{res} strong
signals of Im\chi(q,\omega) tracing an upward dispersion are found and
interpreted as an overdamped collective mode near \omega_{Q}^{res}. In the
normal state, Im\chi(q,\omega) has a broad peak at q=Q. That is, the IC and DIC
signals appear only in the d-wave pairing state. We also study effects of a
small orthorhombic anisotropy, which is intrinsic in untwinned YBCO crystals.
Because of electron-electron correlations favoring d-wave shaped Fermi surface
deformations (dFSD), we expect an enhanced anisotropy of magnetic excitation
spectra. This effect is particularly pronounced for low \delta and at
relatively high temperature. The present theory provides a rather detailed
microscopic explanation of the most salient properties of magnetic excitations
observed in YBCO.
