The adsorption of polyelectrolytes on oppositely charged surfaces is investigated by numerical calculations based on a recent model for polyelectrolyte adsorption by Bohmer et al.,1 which is an extension of the self-consistent-field theory of Scheutjens and Fleer for adsorption of uncharged homopolymers. First, the effects of salt concentration, segment charge, and surface charge density are described for the case of pure electrosorption. It appears that the adsorption always decreases with increasing set concentration. We call this the screening-reduced adsorption regime. The conformation of adsorbed polyelectrolytes with moderate segment charge is rather extended, since they also gain adsorption energy for segments not attached to the surface, due to the long range character of the electrostatic interaction. The polyelectrolyte can be displaced from the surface at a certain critical salt concentration, c(sc), which depends on the segment charge tau, and the surface charge density sigma0, according to c(sc) is-proportional-to (sigma0tau)10/11 following Muthukumar.2 Our numerical data agree rather well with this. The force balance is changed if the segments also have a specific (short-range, nonelectrostatic) interaction with the surface. Now, the screening-reduced adsorption regime occurs only for very low segment charge and sufficiently high surface charge density. The majority of the cases constitutes the screening-enhanced adsorption regime, where the adsorption increases with increasing ionic strength. A transition from the screening-reduced adsorption regime to the screening-enhanced adsorption regime, or vise versa, can take place if the strength of the nonelectrostatic attraction or the electrostatic interaction, by means of the segment charge or the surface charge density, is varied. In the screening-enhanced adsorption regime, a maximum in the adsorbed amount as a function of the salt concentration can occur if the counterions also have a specific interaction with the surface. The theoretical results agree qualitatively with reported experimental results.