Using density functional theory and an exchange-correlation functional that includes the van der Waals interaction, we study the coadsorption of CO on Ru(0001) saturated with 0.5ML of oxygen. Different coexisting CO coverages are considered that are experimentally motivated, the room temperature coverage consisting in 0.5ML-O+0.25ML-CO (low coverage), the saturation coverage achieved at low temperatures (0.5ML-O+0.375ML-CO, intermediate coverage), and the equally mixed monolayer that is stable according to our calculations but not experimentally observed yet (0.5ML-O+0.5ML-CO, high coverage). For each coverage, we study the competition between the desorption and oxidation of CO on the corresponding optimized structure by analyzing their reaction energies and minimum energy reaction paths. The desorption process is endothermic at all coverages, although the desorption energy decreases as the CO coverage increases. The process itself (and also the reverted adsorption) becomes more involved at the intermediate and high coverages because of the appearance of a physisorption well and concomitant energy barrier separating it from the chemisorbed state. Remarkably, the oxidation of CO, which is endothermic at low coverages, turns exothermic at the intermediate and high coverages. In all cases, the minimum reaction path for oxidation, that involves the chemisorbed and physisorbed CO 2 , is ruled by one of the large energy barriers that protect these molecular states. Altogether, the larger activation energies for oxidation as compared to those for desorption and the extreme complexity of the oxidation against the desorption paths explain that CO desorption dominates over the oxidation in experiments.