Damak M. On the Spectral Theory of Dispersive N-Body Hamiltonians (50K, LATeX 2e) ABSTRACT. In this work we describe a general class of dispersive N-body hamiltonians for which we prove the HWZ theorem and a Mourre estimate outside a closed and countable set of energies called thresholds. As a consequence of the Mourre estimate we prove a strong form of the limiting absorption principle which implies absence of singular continuous spectrum and gives criteria of local smoothness.