on Ru(0001) has been studied in the temperature range between 100 K and 300 K by means of low-temperature scanning tunnelling microscopy (STM). At temperatures below 130 K the existence of a molecular precursor state leads to the formation of dense, disordered islands (partly with a (1×1) configuration). Between 160 K and 170 K the onset of diffusion of the chemisorbed O atoms allows a local ordering process in the adsorbate layer. Above 210 K the system reaches a well-ordered equilibrium state, formed by (2×2) and (2×1) structures. From the analysis of the island density versus adsorption temperature data the diffusion energy for the physisorbed precursor state is estimated.