Co,K/MgO catalysts with 12 wt% of Co and 1.5, 4.5 and 7.5 wt% of K, calcined at 400 degrees C are active for the combustion of diesel soot. Among them, the one containing 4.5 wt% of K is that which burns soot at the lowest temperature (378 degrees C). Coincidentally, this is the catalyst presenting the highest K/Mg and K/O surface ratios in XPS measurements. When the calcination temperature is increased at 500 degrees C, both the solid containing 4.5% of K and the one containing 1.5% as well as the unpromoted catalyst (Co/MgO) noticeably lose activity due to the formation of a solid solution (Co, Mg). However, the solid with the highest K content (7.5 wt%) presents a similar activity at different calcination temperatures (400 degrees C, 500 degrees C and 700 degrees C), It has been found that the activity of these solids is directly related to the reducibility of cobalt, thus indicating that the reaction is carried out by a redox mechanism. Potassium plays different roles in these catalysts: (i) it increases the catalyst-soot contact by increasing surface mobility, (ii) it preserves the reducibility and dispersion of cobalt by improving stability against thermal treatments, and (iii) it favors the oxidation of soot by consuming the carbon to form carbonate species during soot combustion. It was also found that soot with a higher content of sulfur (1050 ppm) is more efficiently burned than that containing low amounts of sulfur (70 ppm). However, the severe sulfation of the catalyst leads to a noticeable loss of activity. In experiments of carbon monoxide oxidation, it was found that conversion is practically total between 400 degrees C and 500 degrees C under the conditions used in this work. The direct impregnation of the soot with either Co or Co and K, showed lower combustion temperatures if compared with the mechanical mixtures of soot and Co/MgO or Co,K/MgO, suggesting that the soot-catalyst contact poses a physical limitation on the oxidation activity. This important result suggests that the soot-catalyst contacting problem is the main difficulty to be overcome in order to obtain useful catalysts. All research effort rewards developing catalyst formulations will be unable to reduce the temperature for combustion until this problem is solved.