  We use a Hamiltonian dynamics to discuss the statistical mechanics of
long-lasting quasi-stationary states particularly relevant for long-range
interacting systems. Despite the presence of an anomalous single-particle
velocity distribution, we find that the Central Limit Theorem implies the
Boltzmann expression in Gibbs' $\Gamma$-space. We identify the nonequilibrium
sub-manifold of $\Gamma$-space characterizing the anomalous behavior and show
that by restricting the Boltzmann-Gibbs approach to this sub-manifold we obtain
the statistical mechanics of the quasi-stationary states.
