The adsorption of highly charged flexible polycations and polyanions on a charged cylindrical substrate is investigated by means of Monte Carlo simulations. A detailed structural study, including monomer and fluid charge distributions, is provided. The influence of a short-range attraction between the polycation and negatively charged substrate is also considered. We demonstrate that the building up of multilayer structures is highly prohibited mainly due to the high entropy penalty stemming from the low dimensionality of the substrate at strong curvature. (C) 2003 American Institute of Physics.