The interaction of gas phase atomic hydrogen with chemisorbed oxygen on Ru(001) and RuOx films has been investigated by means of Auger electron spectroscopy and thermal desorption spectroscopy at surface temperatures between 120 and 320 K. Although molecular hydrogen does not adsorb on oxygen saturated Ru(001) or RuOx films even at 120 K, atomic hydrogen reacts with oxygen on Ru(001) surfaces, and both D-2 and D2O desorb at temperatures below 500 g. The 2D(gas)+O-ad->D2Ogas reaction is approximately six times faster at 310 K than at 120 K. For RuOx films, a unity reaction probability was found at oxygen coverages above 3 monolayers (ML), while it decreased to 0.4 at theta(0) < 3 ML. Such variation can be attributed to a change in the structure of the oxide film. The reaction probably follows an Eley-Rideal mechanism where gas phase atomic hydrogen reacts with oxygen prior to thermal accommodation within the surface. The desorption of water is the rate limiting step at surface temperatures below 200 K, whereas the formation of water is the rate limiting step at higher temperatures.