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We present a study of the dynamical spin susceptibility in the pseudogapregion of the high-T$_c$ cuprate superconductors. We analyze and compare theformation 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 theresonance's frequency and momentum dependence in all three states revealssignificant differences between them. In particular, in the DDW state, we findthat a nearly dispersionless resonance excitation exists only in a narrowregion around ${\bf Q}=(\pi,\pi)$. At the same time, in the coexisting DDW andDSC state, the dispersion of the resonance peak near ${\bf Q}$ is significantlychanged from that in the pure DSC state. Away from $(\pi,\pi)$, however, wefind that the form and dispersion of the resonance excitation in the coexistingDDW and DSC state and pure DSC state are quite similar. Our results demonstratethat a detailed experimental measurement of the resonance's dispersion allowsone to distinguish between the underlying phases - a DDW state, a DSC state, ora coexisting DDW and DSC state - in which the resonance peak emerges.

Dynamical spin susceptibility and the resonance peak in the pseudogap region of the underdoped cuprate superconductors