  We present a study of the dynamical spin susceptibility in the pseudogap
region of the high-T$_c$ cuprate superconductors. We analyze and compare the
formation of the so-called resonance peak, in three different ordered states:
the $d_{x^2-y^2}$-wave superconducting (DSC) phase, the $d$-density wave (DDW)
state, and a phase with coexisting DDW and DSC order. An analysis of the
resonance's frequency and momentum dependence in all three states reveals
significant differences between them. In particular, in the DDW state, we find
that a nearly dispersionless resonance excitation exists only in a narrow
region around ${\bf Q}=(\pi,\pi)$. At the same time, in the coexisting DDW and
DSC state, the dispersion of the resonance peak near ${\bf Q}$ is significantly
changed from that in the pure DSC state. Away from $(\pi,\pi)$, however, we
find that the form and dispersion of the resonance excitation in the coexisting
DDW and DSC state and pure DSC state are quite similar. Our results demonstrate
that a detailed experimental measurement of the resonance's dispersion allows
one to distinguish between the underlying phases - a DDW state, a DSC state, or
a coexisting DDW and DSC state - in which the resonance peak emerges.
