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We examine the Hamiltonian structures of some Calogero-Moser and Ruijsenaars-Schneider N-body integrable models. We propose explicit formulations of the bihamiltonian structures for the discrete models, and field-theoretical realizations of these structures. We discuss the relevance of these realizations as collective-field theory for the discrete models.doi:10.1088/1751-8113/43/18/185201 fatcat:itzfjxob4vfwxc4sm2uytz6oge