  The adsorption of highly \textit{oppositely} charged flexible
polyelectrolytes (PEs) on a charged planar substrate is investigated by means
of Monte Carlo (MC) simulations. We study in detail the equilibrium structure
of the first few PE layers. The influence of the chain length and of a (extra)
non-electrostatic short range attraction between the polycations and the
negatively charged substrate is considered. We show that the stability as well
as the microstructure of the PE layers are especially sensitive to the strength
of this latter interaction. Qualitative agreement is reached with some recent
experiments.
