Using a versatile Co-60 radiation aging facility, we have exposed commercial polystyrene samples to a series of dose rates ranging from 18 to 278 Gy/h at both 22°C and 60°C. For exposures in air, a diffusion-limited oxidation band occurs on the outsides of the samples; at a given dose rate, the thickness of this band is approximately independent of dose (up to at least 400 kGy). Modelling of the diffusion-limited oxidation allows us to estimate the oxygen consumed versus dose and dose-rate. Surprisingly, the results at 22°C indicate a `negative' dose-rate effect, where the consumption rate is lower at dose rates below approximately 100 Gy/h than at dose rates above this level. Results from UV/VIS spectroscopy are consistent with this `negative' dose-rate effect, as are oxygen bleaching rates through non-oxidized regions of samples. Analyses of the bleaching rates allow quantitative estimates of the oxygen consumed during subsequent annealing of material aged under inert conditions. When air is present during irradiation, the oxygen consumption is approximately an order of magnitude greater than that measured during post-irradiation bleaching of inert samples. This indicates the likely existence of short-lived radicals which react with oxygen if it is present when they are formed.