The interaction of oxygen and different coverages of potassium on Ru(001) has been investigated by thermal desorption spectroscopy (TDS), metastable quenching spectroscopy (MQS), electron stimulated desorption spectroscopy (ESD), and work-function change measurements. The results show that this is a complex surface system with several different oxides forming, depending on the surface stoichiometry and temperature. While we cannot uniquely identify all the surface species, our interpretation of the present data combined with previous information is as follows. For potassium coverages up to about three monolayers (theta-K almost-equal-to 1), exposure to oxygen initially gives oxygen atoms on the surface. Further exposure produces some surface monoxide ions O2-, which are converted with additional exposure to superoxide ions O2- and possibly peroxide ions O2(2-). Thermal annealing causes strong changes in the surface oxide composition. and with potassium multilayers (theta-K almost-equal-to 10) all the oxides diffuse beneath the K surface layer with annealing to only 300 K. K2O and K2O2 are found to desorb together in the 600-700 K region.