  We prove a generalized version of the RAGE theorem for N-body quantum
systems. The result states that only bound states of systems with $0\leq n\leq
N$ particles persist in the long time average. The limit is formulated by means
of an appropriate weak topology for many-body systems, which was introduced by
the second author in a previous work, and is based on reduced density matrices.
This topology is connected to the weak-* topology of states on the algebras of
canonical commutation or anti-commutation relations, and we give a formulation
of our main result in this setting.
