Thermal desorption spectroscopy (TDS), along with Auger electron spectroscopy, was used to study the desorption of H-2 and CO from baked 304 and 347 stainless-steel samples exposed only to residual gases. Both 347 and 304 samples gave identical TDS spectra. The spectra for CO contained a sharp leading peak centered in the temperature range 410-440-degrees-C and an exponentially increasing part for temperatures higher than 500-degrees-C, with a small peak around 600-degrees-C appearing as a shoulder. The leading peak followed a second-order desorption behavior with an activation energy of 28 +/- 2 kcal/mol, suggesting that the rate-limiting step for this peak is most likely a surface reaction that produces the CO molecules in the surface layer. The amount of desorbed CO corresponding to this peak was approximately 0.5 x 10(14) molecules/cm2. The exponentially rising part of the CO spectrum appeared to originate from a bulk diffusion process. The TDS spectrum for H-2 consisted of a main peak centered also in the temperature range 410-440-degrees-C, with two small peaks appearing as shoulders at approximately 500 and 650-degrees-C. The main peak in this case also displayed a second-order behavior with an activation energy of 14 +/- 2 kcal/mol. The amount of desorbed H-2, approximately 1.9 x 10(15) molecules/cm2, appeared to be independent of the concentration of hydrogen in the bulk, indicating that the majority of the desorbed H-2 originated from the surface layer.