We give further results on the approach to equilibrium of a chain of coupled nonlinear oscillators when the energy is initially fed only to the longest-wave-length modes. We show that the intrinsic time scale for numerical simulations strongly depends upon the initial conditions, increasing as the coupling constant and/or the total energy are lowered. As a consequence, the nonequilibrium spectrum may persist for an extremely large number of computer run steps and may be mistaken as a stationary state.