Monte Carlo simulations of CO/MgO(001) show that below 41 K the CO molecules form a c(4x2) structure with six molecules per unit cell distributed into two kinds of adsorption sites: a perpendicular site and a tilted site (polar angle of 31 degrees). Both sites are localized near Mg2+ ions. The occupancy of perpendicular sites to tilted sites occurs in the ratio of 1:2. At 41 K the c(4x2) phase undergoes a phase transition into a less dense, disordered phase accompanied by the expulsion of some molecules to form a partial second layer. The density of the remaining disordered layer is the same as for a p(3x2) phase and portions of the disordered layer show regions of short range ordering with either the c(4x2) or p(3x2) structures. The p(3x2) phase contains four molecules per unit cell and also consists of perpendicular and tilted sites, but in the ratio of 1:1. This structure was found to be stable up to 50 K after which the expulsion of some molecules and disordering of the layer occurred. A model to test the relative stability of these two phases by examining the difference in Gibbs free energy is constructed and shows that below 41 K the c(4x2) phase is the most stable but above 41 K the p(3x2) phase is the most stable. However, at low pressures the model suggests that the p(3x2) phase will not be observed and the layer will instead transform from the c(4x2) phase to a disordered phase at 41 K. This result reconciles the findings of low-energy electron diffraction (LEED) experiments [p(3x2) phase observed] with those of helium atom scattering (HAS) and polarization infrared spectroscopy (PIRS) experiments (disordered phase observed). It is proposed that the c(4x2)--> p(3x2) transition is part of an infinite sequence of transitions involving (nx2)-type structures which, under suitable conditions of temperature and pressure, constitutes an example of the devil＇s staircase phenomenon. Such a phenomenon has been suggested by previous LEED experiments. (C) 2000 American Institute of Physics. [S0021-9606(00)70611-8].