The electrosorption of Ag onto single-crystal copper (0 0 1) electrodes is studied by Monte Carlo (MC) simulations. An effective Ising model is employed with energetic parameters derived from N-body tight-binding interatomic potentials. Due to the attractive interactions between adsorbate atoms, the equilibrium isotherms present a first-order phase transition at sufficiently low temperatures. Using a dynamic MC algorithm, we study the kinetics of adsorption following sudden potential steps between the low and high branches of the isotherm. We compare these kinetics to those obtained within a mean-field approximation. The MC kinetics are dominated by nucleation and growth processes and are well described by the Kolmogorov-Johnson-Mehl-Avrami (KJMA) equation. We show how some improvements of the classical nucleation theory allow us to derive the physical quantities appearing in this equation, such as the nucleation and the growth rate, from the energetic parameters of the atomistic model. (C) 2003 Elsevier B.V. All rights reserved.