Asymmetric electrolytes consisting of highly charged spherical macroions and small ions representing an aqueous solution of ionic surfactant micelles have been studied at different macroion concentrations by means of Monte Carlo simulations. The model system comprises macroions with 60 elementary charges and either monovalent, divalent, or trivalent counterions interacting solely through hard-core and Coulomb forces. Thermodynamic and structural properties are examined, and the effects of the counterion valency are discussed. For the lowest electrostatic macroion-counterion coupling (monovalent counterions), the macroions are well separated and an effective repulsive potential is acting between them. At stronger electrostatic coupling (divalent counterions), the double-layer repulsion between the macroions is strongly reduced and at short separations the attractive force becomes comparable to the double-layer repulsion. At even stronger coupling (trivalent counterions), the attractive correlation force between the macroions dominates and causes the solution to separate into two fluid phases of highly different density of the electrolyte. Our results differ quantitatively from the mean-field Derjaguin-Landau-Verwey-Overbeek (DLVO) theory, one of the cornerstones of colloid science, which predicts a purely repulsive electrostatic force among like-charged colloidal particles under all conditions. At the same time, our results are consistent with similar finding of an attraction of electrostatic origin between two similarly charged planar surfaces at sufficiently large electrostatic coupling. A detailed analysis of the counterion distribution in the neighborhood of two macroions close to each other has also been performed for divalent counterions. Finally, the effect of salt addition has also been examined. (C) 2000 American Institute of Physics. [S0021-9606(00)50507-8].