TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Process Details : The process comprises a preliminary treatment, T1, for elimination of CO2, leaving an overall CO2 content of at least 200 vppm. This is followed by a purification treatment T2 , which involves a catalytic oxidation of CO by O2 and/or H2O to obtain no more than 50 vppm of CO, then desulfuration of the HC cut without secondary elimination of CO2, in the presence of a current of the purified H2 ; alternatively, a treatment T3 can be carried out, which is a catalytic methanation of CO by H2 followed directly, and without elimination of CO2, by a desulfuration of the HC cut in the presence of the purified H2. The process comprises a recycling of H2, REC, and also incorporates a purge gas WGAS to avoid concentration of impurities ; this maintains a CO content less than 50 vppm and COx content greater than 120 vppm. The catalyst for the process comprises an element of group VIII, and, optionally, of group VIB ; the group VIII element is Ni, Co or Fe, and the group VIB element is Mo or W ; more preferably the catalytst comprises Co and W. The operating pressure is 0.5 - 5 Mpa, the ratio of flow rates H2 / HC is 50 - 800 l/l and the temperature is 200 - 400degreesC. EXAMPLE - (2) comparative : A pilot plant of 200 ml capacity was charged with 100 ml of a Co/Mo catalyst in sulfurised form. The treated charge was a petrol A from a catalytic cracking unit ; this was depentanised , leaving a C6+ fraction for treatment.This contained 425 ppm of S and had a bromine index of 49 g/100 g, with a boiling range of 61 - 229degreesC. To measure the influence of CO and CO2 on the catalyst performance, a supply of H2 containing 100 vppm of CO and 350 vppm of CO2 was used.The H2 was mixed with the petrol A , the mixture thus obtained having CO and CO2 contents of 65 vppm and 228 vppm respectively. The results of trials at 260, 280 and 300degreesC for S contents(ppm) were 103, 25 and 13 respectively, with bromine indices of 38.4, 32.3 and 23.6. This indicated a degradation of hydrodesulfurising activity but no significant change in hydrogenating activity of the catalyst. 3) Another trial(invention) was carried out using a purified H2 gas which contained 17 vppm of CO and 430 vppm of CO2.The gas was mixed with the petrol A and tested under similar operating conditions ; the mixture thus obtained had a CO content of 11 vppm and CO2 content of 283 vppm. The results at 260, 280 and 300degreesC for S contents(ppm) were 71, 20 and 10 respectively, and the bromine indices were 38.1, 31.8 and 22.9. The pre-treated H2 thus significantly improved the hydrodesulfuration activity of the catalyst, and the harmful effect of the CO was inhibited without the necessity to eliminate all of the CO2 present.