  The time evolution of the correlation functions of an ensemble of anharmonic
N-component oscillators with O(N) symmetry is described by a flow equation,
exact up to corrections of order $1/N^2$. We find effective irreversibility.
Nevertheless, analytical and numerical investigation reveals that the system
does not reach thermal equilibrium for large times, even when $N\to \infty$.
Depending on the initial distribution, the dynamics is asymptotically stable or
it exhibits growing modes which break the conditions for the validity of the
1/N expansion for large time. We investigate both classical and quantum
systems, the latter being the limit of an O(N) symmetric scalar quantum field
theory in zero spatial dimensions.
