An annealing process has been applied to three samples of vinyl alcohol-ethylene (VAE) copolymers, richer in the former comonomer. The effect of such a process on the structure and on the relaxation mechanisms is studied. The structure of the three VAE copolymers has changed slightly. Nevertheless, the viscoelastic relaxation processes have been significantly affected for the thermal treatment. Two additional relaxations have appeared: one of them at temperatures above the relaxation associated to the glass transition, and the other at temperatures below the beta mechanism of these copolymers. The temperature location, intensity, and apparent activation energy of the distinct relaxations found are discussed and compared with those in the original copolymers and the homopolymers, poly(vinyl alcohol) and polyethylene. (C) 2000 John Wiley & Sons, Inc.