  The adsorption of highly \textit{oppositely} charged flexible
polyelectrolytes onto a charged spherical surface is investigated by means of
Monte Carlo simulations in a fashion which resembles the layer-by-layer
deposition technique introduced by Decher. Electroneutrality is insured at each
step by the presence of monovalent counterions (anions and cations). We study
in detail the structure of the \textit{equilibrium} complex. Our investigations
of the first few layer formations strongly suggest that multilayering in
spherical geometry is not possible as an equilibrium process with purely
electrostatic interactions. We especially focus on the influence of specific
(non-electrostatic) short range attractive interactions (e.g., Van der Waals)
on the stability of the multilayers.
