  We study the link between relaxation to the equilibrium and anomalous
superdiffusive motion in a classical N-body hamiltonian system with long-range
interaction showing a second-order phase-transition in the canonical ensemble.
Anomalous diffusion is observed only in a transient out-of-equilibrium regime
and for a small range of energy, below the critical one. Superdiffusion is due
to L\'evy walks of single particles and is checked independently through the
second moment of the distribution, power spectra, trapping and walking time
probabilities. Diffusion becomes normal at equilibrium, after a relaxation time
which diverges with N.
