[en] Motivated by its use in a Two-Beam Accelerator, we have studied a ''steady-state'' FEL; i.e., a periodic but very long structure in which the electron beam energy is replenished once a period with a short induction acceleration unit. We have studied longitudinal particle motion in such a device using a 1-D simulation code. We show that after an initial start-up section, particle detrapping from the pondermotive wave is minimal in a steady-state FEL of several kilometers. A simple linear model of particle diffusion is shown to describe the numerical results quite well